 1.5.1: In Exercises 18, show that and are inverse functions (a) analytical...
 1.5.2: In Exercises 18, show that and are inverse functions (a) analytical...
 1.5.3: In Exercises 18, show that and are inverse functions (a) analytical...
 1.5.4: In Exercises 18, show that and are inverse functions (a) analytical...
 1.5.5: In Exercises 18, show that and are inverse functions (a) analytical...
 1.5.6: In Exercises 18, show that and are inverse functions (a) analytical...
 1.5.7: In Exercises 18, show that and are inverse functions (a) analytical...
 1.5.8: In Exercises 18, show that and are inverse functions (a) analytical...
 1.5.9: In Exercises 912, match the graph of the function with the graph of...
 1.5.10: In Exercises 912, match the graph of the function with the graph of...
 1.5.11: In Exercises 912, match the graph of the function with the graph of...
 1.5.12: In Exercises 912, match the graph of the function with the graph of...
 1.5.13: In Exercises 1316, use the Horizontal Line Test to determine whethe...
 1.5.14: In Exercises 1316, use the Horizontal Line Test to determine whethe...
 1.5.15: In Exercises 1316, use the Horizontal Line Test to determine whethe...
 1.5.16: In Exercises 1316, use the Horizontal Line Test to determine whethe...
 1.5.17: In Exercises 1722, use a graphing utility to graph the function. De...
 1.5.18: In Exercises 1722, use a graphing utility to graph the function. De...
 1.5.19: In Exercises 1722, use a graphing utility to graph the function. De...
 1.5.20: In Exercises 1722, use a graphing utility to graph the function. De...
 1.5.21: In Exercises 1722, use a graphing utility to graph the function. De...
 1.5.22: In Exercises 1722, use a graphing utility to graph the function. De...
 1.5.23: In Exercises 2328, determine whether the function is onetoone on i...
 1.5.24: In Exercises 2328, determine whether the function is onetoone on i...
 1.5.25: In Exercises 2328, determine whether the function is onetoone on i...
 1.5.26: In Exercises 2328, determine whether the function is onetoone on i...
 1.5.27: In Exercises 2328, determine whether the function is onetoone on i...
 1.5.28: In Exercises 2328, determine whether the function is onetoone on i...
 1.5.29: In Exercises 2936, find the inverse function of Graph (by hand) and...
 1.5.30: In Exercises 2936, find the inverse function of Graph (by hand) and...
 1.5.31: In Exercises 2936, find the inverse function of Graph (by hand) and...
 1.5.32: In Exercises 2936, find the inverse function of Graph (by hand) and...
 1.5.33: In Exercises 2936, find the inverse function of Graph (by hand) and...
 1.5.34: In Exercises 2936, find the inverse function of Graph (by hand) and...
 1.5.35: In Exercises 2936, find the inverse function of Graph (by hand) and...
 1.5.36: In Exercises 2936, find the inverse function of Graph (by hand) and...
 1.5.37: In Exercises 37 42, find the inverse function of Use a graphing uti...
 1.5.38: In Exercises 37 42, find the inverse function of Use a graphing uti...
 1.5.39: In Exercises 37 42, find the inverse function of Use a graphing uti...
 1.5.40: In Exercises 37 42, find the inverse function of Use a graphing uti...
 1.5.41: In Exercises 37 42, find the inverse function of Use a graphing uti...
 1.5.42: In Exercises 37 42, find the inverse function of Use a graphing uti...
 1.5.43: In Exercises 43 and 44, use the graph of the function to complete t...
 1.5.44: In Exercises 43 and 44, use the graph of the function to complete t...
 1.5.45: Cost You need 50 pounds of two commodities costing $1.25 and $1.60 ...
 1.5.46: Temperature The formula where represents the Celsius temperature as...
 1.5.47: In Exercises 47 and 48, find over the indicated interval. Use a gra...
 1.5.48: In Exercises 47 and 48, find over the indicated interval. Use a gra...
 1.5.49: Graphical Reasoning In Exercises 4952, (a) use a graphing utility t...
 1.5.50: Graphical Reasoning In Exercises 4952, (a) use a graphing utility t...
 1.5.51: Graphical Reasoning In Exercises 4952, (a) use a graphing utility t...
 1.5.52: Graphical Reasoning In Exercises 4952, (a) use a graphing utility t...
 1.5.53: In Exercises 5358, show that is onetoone on the indicated interva...
 1.5.54: In Exercises 5358, show that is onetoone on the indicated interva...
 1.5.55: In Exercises 5358, show that is onetoone on the indicated interva...
 1.5.56: In Exercises 5358, show that is onetoone on the indicated interva...
 1.5.57: In Exercises 5358, show that is onetoone on the indicated interva...
 1.5.58: In Exercises 5358, show that is onetoone on the indicated interva...
 1.5.59: In Exercises 5962, determine whether the function is onetoone. If ...
 1.5.60: In Exercises 5962, determine whether the function is onetoone. If ...
 1.5.61: In Exercises 5962, determine whether the function is onetoone. If ...
 1.5.62: In Exercises 5962, determine whether the function is onetoone. If ...
 1.5.63: In Exercises 6366, delete part of the domain so that the function t...
 1.5.64: In Exercises 6366, delete part of the domain so that the function t...
 1.5.65: In Exercises 6366, delete part of the domain so that the function t...
 1.5.66: In Exercises 6366, delete part of the domain so that the function t...
 1.5.67: In Exercises 6772, find for the function and realnumber a
 1.5.68: In Exercises 6772, find for the function and realnumber a
 1.5.69: In Exercises 6772, find for the function and realnumber a
 1.5.70: In Exercises 6772, find for the function and realnumber a
 1.5.71: In Exercises 6772, find for the function and realnumber a
 1.5.72: In Exercises 6772, find for the function and realnumber a
 1.5.73: In Exercises 7376, use the functions and to find the indicated value.
 1.5.74: In Exercises 7376, use the functions and to find the indicated value.
 1.5.75: In Exercises 7376, use the functions and to find the indicated value.
 1.5.76: In Exercises 7376, use the functions and to find the indicated value.
 1.5.77: In Exercises 7780, use the functions and to find the indicated func...
 1.5.78: In Exercises 7780, use the functions and to find the indicated func...
 1.5.79: In Exercises 7780, use the functions and to find the indicated func...
 1.5.80: In Exercises 7780, use the functions and to find the indicated func...
 1.5.81: In Exercises 81 and 82, (a) use the graph of the function todetermi...
 1.5.82: In Exercises 81 and 82, (a) use the graph of the function todetermi...
 1.5.83: In Exercises 83 and 84, use the graph of the function to sketch the...
 1.5.84: In Exercises 83 and 84, use the graph of the function to sketch the...
 1.5.85: Numerical and Graphical Analysis In Exercises 85 and 86, (a) use a ...
 1.5.86: Numerical and Graphical Analysis In Exercises 85 and 86, (a) use a ...
 1.5.87: Determine the missing coordinates of the points on the graph of the...
 1.5.88: Determine the missing coordinates of the points on the graph of the...
 1.5.89: In Exercises 8996, evaluate the expression without using a calculat...
 1.5.90: In Exercises 8996, evaluate the expression without using a calculator
 1.5.91: In Exercises 8996, evaluate the expression without using a calculat...
 1.5.92: In Exercises 8996, evaluate the expression without using a calculator
 1.5.93: In Exercises 8996, evaluate the expression without using a calculator
 1.5.94: In Exercises 8996, evaluate the expression without using a calculat...
 1.5.95: In Exercises 8996, evaluate the expression without using a calculator
 1.5.96: In Exercises 8996, evaluate the expression without using a calculat...
 1.5.97: In Exercises 97100, use a calculator to approximate the value. Roun...
 1.5.98: In Exercises 97100, use a calculator to approximate the value. Roun...
 1.5.99: In Exercises 97100, use a calculator to approximate the value. Roun...
 1.5.100: In Exercises 97100, use a calculator to approximate the value. Roun...
 1.5.101: Describe how to find the inverse function of a onetoone function ...
 1.5.102: Describe the relationship between the graph of a functionand the gr...
 1.5.103: Give an example of a function that does not have an inverse function.
 1.5.104: Explain why does not imply that arctan 0 .
 1.5.105: Explain why the domains of the trigonometric functions are restrict...
 1.5.106: Explain how to graph on a graphing utility that does not have the a...
 1.5.107: In Exercises 107 and 108, use a graphing utility to confirm that an...
 1.5.108: In Exercises 107 and 108, use a graphing utility to confirm that an...
 1.5.109: In Exercises 109 and 110, use the properties of inverse trigonometr...
 1.5.110: In Exercises 109 and 110, use the properties of inverse trigonometr...
 1.5.111: In Exercises 111116, evaluate the expression without using a calcul...
 1.5.112: In Exercises 111116, evaluate the expression without using a calcul...
 1.5.113: In Exercises 111116, evaluate the expression without using a calcul...
 1.5.114: In Exercises 111116, evaluate the expression without using a calcul...
 1.5.115: In Exercises 111116, evaluate the expression without using a calcul...
 1.5.116: In Exercises 111116, evaluate the expression without using a calcul...
 1.5.117: In Exercises 117120, solve the equation for x.arcsin3x ) 12
 1.5.118: In Exercises 117120, solve the equation for x.arctan2x 5 1a
 1.5.119: In Exercises 117120, solve the equation for x.arcsin 2x arccos x
 1.5.120: In Exercises 117120, solve the equation for x.arccos x arcsec x
 1.5.121: In Exercises 121 and 122, find the point of intersection of thegrap...
 1.5.122: In Exercises 121 and 122, find the point of intersection of the gra...
 1.5.123: In Exercises 123132, write the expression in algebraic form.tanarct...
 1.5.124: In Exercises 123132, write the expression in algebraic form.sinarcc...
 1.5.125: In Exercises 123132, write the expression in algebraic form.cosarcs...
 1.5.126: In Exercises 123132, write the expression in algebraic form.secarct...
 1.5.127: In Exercises 123132, write the expression in algebraic form.sinarcs...
 1.5.128: In Exercises 123132, write the expression in algebraic form.. cosar...
 1.5.129: In Exercises 123132, write the expression in algebraic form.tanarcs...
 1.5.130: In Exercises 123132, write the expression in algebraic form.
 1.5.131: In Exercises 123132, write the expression in algebraic form.cscarct...
 1.5.132: In Exercises 123132, write the expression in algebraic form.cosarcs...
 1.5.133: In Exercises 133 and 134, fill in the blank.arctan9x arcsin , x > 0c
 1.5.134: In Exercises 133 and 134, fill in the blank.arcsin 36 x26 arccos a
 1.5.135: In Exercises 135 and 136, verify each identity.
 1.5.136: In Exercises 135 and 136, verify each identity.
 1.5.137: In Exercises 137140, sketch the graph of the function. Use a graphi...
 1.5.138: In Exercises 137140, sketch the graph of the function. Use a graphi...
 1.5.139: In Exercises 137140, sketch the graph of the function. Use a graphi...
 1.5.140: In Exercises 137140, sketch the graph of the function. Use a graphi...
 1.5.141: Prove that if and are onetoone functions, then f g1x g1 f 1x.f g
 1.5.142: Prove that if has an inverse function, then f 1 f 1 f.
 1.5.143: Prove that if a function has an inverse function, then the inverse ...
 1.5.144: Prove that a function has an inverse function if and only if it is ...
 1.5.145: True or False? In Exercises 145150, determine whether the statement...
 1.5.146: True or False? In Exercises 145150, determine whether the statement...
 1.5.147: True or False? In Exercises 145150, determine whether the statement...
 1.5.148: True or False? In Exercises 145150, determine whether the statement...
 1.5.149: True or False? In Exercises 145150, determine whether the statement...
 1.5.150: True or False? In Exercises 145150, determine whether the statement...
 1.5.151: Prove that arctan x arctan y arctan x y1 xy, xy 1.f Use this formul...
 1.5.152: Think About It Use a graphing utility to graph fx sin x and gx arcs...
 1.5.153: Let where and the domain is all real numbers such that x . b find f 1
 1.5.154: Determine conditions on the constants and such that the graph of is...
 1.5.155: Determine conditions on the constants a, b, c, and d such that has ...
Solutions for Chapter 1.5: Inverse Functions
Full solutions for Calculus: Early Transcendental Functions  4th Edition
ISBN: 9780618606245
Solutions for Chapter 1.5: Inverse Functions
Get Full SolutionsChapter 1.5: Inverse Functions includes 155 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions , edition: 4. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9780618606245. This expansive textbook survival guide covers the following chapters and their solutions. Since 155 problems in chapter 1.5: Inverse Functions have been answered, more than 41562 students have viewed full stepbystep solutions from this chapter.

Arctangent function
See Inverse tangent function.

Circle
A set of points in a plane equally distant from a fixed point called the center

Commutative properties
a + b = b + a ab = ba

Complex fraction
See Compound fraction.

Damping factor
The factor Aea in an equation such as y = Aeat cos bt

Data
Facts collected for statistical purposes (singular form is datum)

Decreasing on an interval
A function f is decreasing on an interval I if, for any two points in I, a positive change in x results in a negative change in ƒ(x)

Difference of complex numbers
(a + bi)  (c + di) = (a  c) + (b  d)i

Empty set
A set with no elements

Equivalent equations (inequalities)
Equations (inequalities) that have the same solutions.

Extraneous solution
Any solution of the resulting equation that is not a solution of the original equation.

Factoring (a polynomial)
Writing a polynomial as a product of two or more polynomial factors.

Feasible points
Points that satisfy the constraints in a linear programming problem.

Finite series
Sum of a finite number of terms.

Limit at infinity
limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x: q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large

Linear function
A function that can be written in the form ƒ(x) = mx + b, where and b are real numbers

Newton’s law of cooling
T1t2 = Tm + 1T0  Tm2ekt

Reflection across the xaxis
x, y and (x,y) are reflections of each other across the xaxis.

Upper bound test for real zeros
A test for finding an upper bound for the real zeros of a polynomial.

Vertical translation
A shift of a graph up or down.