 0.4.1: In each part, determine whether the function f is onetoone.(a) f(...
 0.4.2: A student enters a number on a calculator, doubles it, adds 8to the...
 0.4.3: If (3, 2) is a point on the graph of an odd invertible functionf , ...
 0.4.4: In each part, determine the exact value without using a calculating...
 0.4.5: In each part, determine the exact value without using a calculating...
 0.4.6: A face of a broken clock lies in the xyplane with the centerof the...
 0.4.7: (a) The accompanying figure shows the graph of a functionf over its...
 0.4.8: (a) Explain why the function f graphed in the accompanyingfigure ha...
 0.4.9: 916 Find a formula for f 1(x). f(x) = 7x 6
 0.4.10: 916 Find a formula for f 1(x). f(x) = x + 1x 1
 0.4.11: 916 Find a formula for f 1(x). f(x) = 3x3 5
 0.4.12: 916 Find a formula for f 1(x). f(x) = 5 4x + 2
 0.4.13: 916 Find a formula for f 1(x). f(x) = 3/x2, x < 0
 0.4.14: 916 Find a formula for f 1(x). f(x) = 5/(x2 + 1), x 0
 0.4.15: 916 Find a formula for f 1(x). f(x) =5/2 x, x < 21/x, x 2
 0.4.16: 916 Find a formula for f 1(x). f(x) =2x, x 0x2, x> 0
 0.4.17: 1720 Find a formula for f 1(x), and state the domain of the functio...
 0.4.18: 1720 Find a formula for f 1(x), and state the domain of the functio...
 0.4.19: 1720 Find a formula for f 1(x), and state the domain of the functio...
 0.4.20: 1720 Find a formula for f 1(x), and state the domain of the functio...
 0.4.21: Let f(x) = ax2 + bx + c, a > 0. Find f 1 if the domainof f is restr...
 0.4.22: he formula F = 95C + 32, where C 273.15 expressesthe Fahrenheit tem...
 0.4.23: (a) One meter is about 6.214 104 miles. Find a formulay = f(x) that...
 0.4.24: Let f(x) = x2, x > 1, and g(x) = x.(a) Show that f(g(x)) = x, x > 1...
 0.4.25: (a) Show that f(x) = (3 x)/(1 x) is its own inverse.(b) What does t...
 0.4.26: Sketch the graph of a function that is onetoone on(, +), yet not ...
 0.4.27: Let f(x) = 2x3 + 5x + 3. Find x if f 1(x) = 1.
 0.4.28: Let f(x) = x3x2 + 1. Find x if f f1x =2
 0.4.29: Prove that if a2 + bc = 0, then the graph off(x) = ax + bcx ais sym...
 0.4.30: (a) Prove: If f and g are onetoone, then so is the compositionf g...
 0.4.31: 3134 TrueFalse Determine whether the statement is true or false. Ex...
 0.4.32: 3134 TrueFalse Determine whether the statement is true or false. Ex...
 0.4.33: 3134 TrueFalse Determine whether the statement is true or false. Ex...
 0.4.34: 3134 TrueFalse Determine whether the statement is true or false. Ex...
 0.4.35: Given that = tan1 43, find the exact values of sin ,cos , cot , sec...
 0.4.36: Given that = sec1 2.6, find the exact values of sin ,cos , tan , co...
 0.4.37: For which values of x is it true that(a) cos1(cos x) = x (b) cos(co...
 0.4.38: 3839 Find the exact value of the given quantity. sec sin1 34
 0.4.39: 3839 Find the exact value of the given quantity. sin 2 cos1 35
 0.4.40: 4041 Complete the identities using the triangle method (Figure 0.4....
 0.4.41: 4041 Complete the identities using the triangle method (Figure 0.4....
 0.4.42: (a) Use a calculating utility set to radian measure to maketables o...
 0.4.43: In each part, sketch the graph and check your work with agraphing u...
 0.4.44: The law of cosines states thatc2 = a2 + b2 2ab cos where a, b, and ...
 0.4.45: 4546 Use a calculating utility to approximate the solution of each ...
 0.4.46: 4546 Use a calculating utility to approximate the solution of each ...
 0.4.47: (a) Use a calculating utility to evaluate the expressionssin1(sin1 ...
 0.4.48: A soccer player kicks a ball with an initial speed of 14m/s at an a...
 0.4.49: 4950 The function cot1 x is defined to be the inverse ofthe restric...
 0.4.50: 4950 The function cot1 x is defined to be the inverse ofthe restric...
 0.4.51: Most scientific calculators have keys for the values of onlysin1 x,...
 0.4.52: An Earthobserving satellite has horizon sensors that canmeasure th...
 0.4.53: The number of hours of daylight on a given day at a givenpoint on t...
 0.4.54: A camera is positioned x feet from the base of a missilelaunching p...
 0.4.55: An airplane is flying at a constant height of 3000 ft abovewater at...
 0.4.56: Prove:(a) sin1(x) = sin1 x(b) tan1(x) = tan1 x.
 0.4.57: Prove:(a) cos1(x) = cos1 x(b) sec1(x) = sec1 x.
 0.4.58: Prove:(a) sin1 x = tan1 x 1 x2(x < 1)(b) cos1 x = 2 tan1 x 1 x2(...
 0.4.59: Prove:tan1 x + tan1 y = tan1 x + y1 xy provided /2 < tan1 x + tan1 ...
 0.4.60: Use the result in Exercise 59 to show that(a) tan1 12 + tan1 13 = /...
 0.4.61: Use identities (10) and (13) to obtain identity (17).
 0.4.62: Prove: A onetoone function f cannot have two different inverses.
Solutions for Chapter 0.4: INVERSE FUNCTIONS; INVERSE TRIGONOMETRIC FUNCTIONS
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 0.4: INVERSE FUNCTIONS; INVERSE TRIGONOMETRIC FUNCTIONS
Get Full SolutionsChapter 0.4: INVERSE FUNCTIONS; INVERSE TRIGONOMETRIC FUNCTIONS includes 62 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10. This expansive textbook survival guide covers the following chapters and their solutions. Since 62 problems in chapter 0.4: INVERSE FUNCTIONS; INVERSE TRIGONOMETRIC FUNCTIONS have been answered, more than 39795 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691.

Bounded below
A function is bounded below if there is a number b such that b ? ƒ(x) for all x in the domain of f.

Direction of an arrow
The angle the arrow makes with the positive xaxis

Equal complex numbers
Complex numbers whose real parts are equal and whose imaginary parts are equal.

Equivalent vectors
Vectors with the same magnitude and direction.

Infinite limit
A special case of a limit that does not exist.

Law of sines
sin A a = sin B b = sin C c

Linear factorization theorem
A polynomial ƒ(x) of degree n > 0 has the factorization ƒ(x) = a(x1  z1) 1x  i z 22 Á 1x  z n where the z1 are the zeros of ƒ

Mode of a data set
The category or number that occurs most frequently in the set.

Natural numbers
The numbers 1, 2, 3, . . . ,.

Odd function
A function whose graph is symmetric about the origin (ƒ(x) = ƒ(x) for all x in the domain of f).

Onetoone function
A function in which each element of the range corresponds to exactly one element in the domain

Partial sums
See Sequence of partial sums.

Probability function
A function P that assigns a real number to each outcome O in a sample space satisfying: 0 … P1O2 … 1, P12 = 0, and the sum of the probabilities of all outcomes is 1.

Quadrantal angle
An angle in standard position whose terminal side lies on an axis.

Quadratic regression
A procedure for fitting a quadratic function to a set of data.

Response variable
A variable that is affected by an explanatory variable.

Richter scale
A logarithmic scale used in measuring the intensity of an earthquake.

Triangular number
A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.

Unit vector
Vector of length 1.

Unit vector in the direction of a vector
A unit vector that has the same direction as the given vector.