 10.1: Let h(x)=2x and k(x) = x2. Find formulas for h(k(x)) and k(h(x)).
 10.2: Find formulas for the functions in Exercises 27 and simplify. Let f...
 10.3: Find formulas for the functions in Exercises 27 and simplify. Let f...
 10.4: Find formulas for the functions in Exercises 27 and simplify. Let f...
 10.5: Find formulas for the functions in Exercises 27 and simplify. Let f...
 10.6: Find formulas for the functions in Exercises 27 and simplify. Let f...
 10.7: Find formulas for the functions in Exercises 27 and simplify. Let f...
 10.8: Using Tables 10.19 and 10.20, complete Table 10.21:
 10.9: For each of the following functions, use a graph to decide whether ...
 10.10: Find the inverses of the functions in Exercises 1022.h(x) = 12x3
 10.11: Find the inverses of the functions in Exercises 1022.h(x) = x 2x + 1
 10.12: Find the inverses of the functions in Exercises 1022.k(x)=3 e2x
 10.13: Find the inverses of the functions in Exercises 1022.g(x) = e3x+1
 10.14: Find the inverses of the functions in Exercises 1022.n(x) = log(x 3)
 10.15: Find the inverses of the functions in Exercises 1022.h(x) = ln(1 2x)
 10.16: Find the inverses of the functions in Exercises 1022.h(x) = x x + 1
 10.17: Find the inverses of the functions in Exercises 1022.g(x) = x 2 2x + 3
 10.18: Find the inverses of the functions in Exercises 1022.f(x) = 4 7x 4 x
 10.19: Find the inverses of the functions in Exercises 1022.f(x) = x + 3 11 x
 10.20: Find the inverses of the functions in Exercises 1022.f(x) = ln 1 + 1 x
 10.21: Find the inverses of the functions in Exercises 1022.s(x) = 3 2 + l...
 10.22: Find the inverses of the functions in Exercises 1022.q(x) = ln(x + ...
 10.23: In Exercises 2328, state whether the function is invertible. If so,...
 10.24: In Exercises 2328, state whether the function is invertible. If so,...
 10.25: In Exercises 2328, state whether the function is invertible. If so,...
 10.26: In Exercises 2328, state whether the function is invertible. If so,...
 10.27: In Exercises 2328, state whether the function is invertible. If so,...
 10.28: In Exercises 2328, state whether the function is invertible. If so,...
 10.29: Check that h1(h(x)) = x if h(x) = 1 x x for 0 < x 1 and h1 (x) = 1 ...
 10.30: Suppose f(x) = x 2x + 1 . Find a formula for f1(x).
 10.31: In Exercises 3136, find simplified formulas if f(x) = ex, g(x)=2x 1...
 10.32: In Exercises 3136, find simplified formulas if f(x) = ex, g(x)=2x 1...
 10.33: In Exercises 3136, find simplified formulas if f(x) = ex, g(x)=2x 1...
 10.34: In Exercises 3136, find simplified formulas if f(x) = ex, g(x)=2x 1...
 10.35: In Exercises 3136, find simplified formulas if f(x) = ex, g(x)=2x 1...
 10.36: In Exercises 3136, find simplified formulas if f(x) = ex, g(x)=2x 1...
 10.37: Find formulas for the following functions, given that f(x) = x2+x, ...
 10.38: In Exercises 3840, find simplified formulas if u(x) = 1 1 + x2 , v(...
 10.39: In Exercises 3840, find simplified formulas if u(x) = 1 1 + x2 , v(...
 10.40: In Exercises 3840, find simplified formulas if u(x) = 1 1 + x2 , v(...
 10.41: In Exercises 4146, find a simplified formula for the function. Let ...
 10.42: In Exercises 4146, find a simplified formula for the function. Let ...
 10.43: In Exercises 4146, find a simplified formula for the function. Let ...
 10.44: In Exercises 4146, find a simplified formula for the function. Let ...
 10.45: In Exercises 4146, find a simplified formula for the function. Let ...
 10.46: In Exercises 4146, find a simplified formula for the function. Let ...
 10.47: In Exercises 4750 find simplified formulas if f(x) = x3/2, g(x) = (...
 10.48: In Exercises 4750 find simplified formulas if f(x) = x3/2, g(x) = (...
 10.49: In Exercises 4750 find simplified formulas if f(x) = x3/2, g(x) = (...
 10.50: In Exercises 4750 find simplified formulas if f(x) = x3/2, g(x) = (...
 10.51: Complete Table 10.22 if r(t) = q(p(t)).
 10.52: Complete Table 10.23, Table 10.24, and Table 10.25 given that h(x) ...
 10.53: Decompose the functions in 5360 into two new functions, u and v, wh...
 10.54: Decompose the functions in 5360 into two new functions, u and v, wh...
 10.55: Decompose the functions in 5360 into two new functions, u and v, wh...
 10.56: Decompose the functions in 5360 into two new functions, u and v, wh...
 10.57: Decompose the functions in 5360 into two new functions, u and v, wh...
 10.58: Decompose the functions in 5360 into two new functions, u and v, wh...
 10.59: Decompose the functions in 5360 into two new functions, u and v, wh...
 10.60: Decompose the functions in 5360 into two new functions, u and v, wh...
 10.61: Using your knowledge of the absolute value function, explain in a f...
 10.62: Graph the following functions for 2 x 2. (a) f(x) = sin x (b) g(x) ...
 10.63: Graph the following functions for 2 x 2. (a) f(x) = sin x (b) g(x) ...
 10.64: Let f(x) = 1 x and g(x) = sin x. Calculate the domain of f(g(x)) an...
 10.65: Suppose that h(x) = f(g(x)), and that f is invertible. Complete the...
 10.66: In 6667, a population is given by the formula P = f(t) = 20 + 0.4t ...
 10.67: In 6667, a population is given by the formula P = f(t) = 20 + 0.4t ...
 10.68: Let P = f(t) = 14 2t/12 give the size in 1000s of an animal populat...
 10.69: If t = g(v) represents the time in hours it takes to drive to the n...
 10.70: Let f(x) = ex. Solve each of the following equations exactly for x....
 10.71: Simplify the expression cos2(arcsin t), using the property that inv...
 10.72: Solve the equations in 7277 exactly. Use an inverse function when a...
 10.73: Solve the equations in 7277 exactly. Use an inverse function when a...
 10.74: Solve the equations in 7277 exactly. Use an inverse function when a...
 10.75: Solve the equations in 7277 exactly. Use an inverse function when a...
 10.76: Solve the equations in 7277 exactly. Use an inverse function when a...
 10.77: Solve the equations in 7277 exactly. Use an inverse function when a...
 10.78: Let Q = f(t) = 20(0.96)t/3 be the number of grams of a radioactive ...
 10.79: (a) What is the formula for the area of a circle in terms of its ra...
 10.80: A company believes there is a linear relationship between the consu...
 10.81: Use Figure 10.34. (a) Evaluate f(g(a)). (b) Evaluate g(f(c)). (c) E...
 10.82: Use Table 10.26 to make tables of values for the following function...
 10.83: For 8387, let p(x)=2x 3 q(x) = x 3 r(x) = 2x 1 2x + 1 s(x)=(x 1)2Fi...
 10.84: For 8387, let p(x)=2x 3 q(x) = x 3 r(x) = 2x 1 2x + 1 s(x)=(x 1)2Fi...
 10.85: For 8387, let p(x)=2x 3 q(x) = x 3 r(x) = 2x 1 2x + 1 s(x)=(x 1)2So...
 10.86: For 8387, let p(x)=2x 3 q(x) = x 3 r(x) = 2x 1 2x + 1 s(x)=(x 1)2Fi...
 10.87: For 8387, let p(x)=2x 3 q(x) = x 3 r(x) = 2x 1 2x + 1 s(x)=(x 1)2Gr...
 10.88: Let f(x) = ex. For each of the following, use the rules of logarith...
 10.89: Let u(x) = sin x, v(x) = cos x, and w(x) = x2. (a) Let f(x) = sin2x...
 10.90: Using Figures 10.35 and 10.36, graph the functions in 9093.f(x) g(x)
 10.91: Using Figures 10.35 and 10.36, graph the functions in 9093.f(g(x))
 10.92: Using Figures 10.35 and 10.36, graph the functions in 9093.g(f(x))
 10.93: Using Figures 10.35 and 10.36, graph the functions in 9093.g(f(x 2))
 10.94: Using Figure 10.37, match the functions (a)(g) and graphs (I)(IV). ...
 10.95: (a) On the same set of axes, graph f(x)=(x 4)2 2 and g(x) = (x 2)2 ...
 10.96: Figure 10.38 shows a weight attached to the end of a spring that is...
 10.97: (a) Find possible formulas for the functions in Figure 10.39. (b) L...
 10.98: Use Figure 10.40 to graph c(x) = a(x) b(x). [Hint: There is not eno...
 10.99: Use Figure 10.41 to graph the following functions. (a) y = g(x) 3 (...
 10.100: Describe the similarities and differences between the graphs of y =...
 10.101: Is the following statement true or false? If f(x) g(x) is an odd fu...
 10.102: In 102103, find a simplified formula for g given that f(x) = x2 + 5...
 10.103: In 102103, find a simplified formula for g given that f(x) = x2 + 5...
 10.104: Assume that f(x)=3 9x and that g(x)=3x. (a) If f(x) = h (g(x)), fin...
 10.105: In calculus, it is often necessary to write functions in the form y...
 10.106: Currency traders often move investments from one country to another...
 10.107: Letting h(x) = f(x) + g(x), say which of the following statements m...
 10.108: (a) Is the sum of two even functions even, odd, or neither? Justify...
 10.109: In 109112, let f(x) be an increasing function and let g(x) be a dec...
 10.110: In 109112, let f(x) be an increasing function and let g(x) be a dec...
 10.111: In 109112, let f(x) be an increasing function and let g(x) be a dec...
 10.112: In 109112, let f(x) be an increasing function and let g(x) be a dec...
 10.113: For a positive integer x, let f(x) be the remainder obtained by div...
 10.114: Suppose that f, g, and h are invertible and that f(x) = g(h(x)). Fi...
 10.115: The von Bertalanffy growth model predicts the mean length L of fish...
Solutions for Chapter 10: COMPOSITIONS, INVERSES, AND COMBINATIONS OF FUNCTIONS
Full solutions for Functions Modeling Change: A Preparation for Calculus  4th Edition
ISBN: 9780470484753
Solutions for Chapter 10: COMPOSITIONS, INVERSES, AND COMBINATIONS OF FUNCTIONS
Get Full SolutionsThis textbook survival guide was created for the textbook: Functions Modeling Change: A Preparation for Calculus , edition: 4. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 10: COMPOSITIONS, INVERSES, AND COMBINATIONS OF FUNCTIONS includes 115 full stepbystep solutions. Functions Modeling Change: A Preparation for Calculus was written by and is associated to the ISBN: 9780470484753. Since 115 problems in chapter 10: COMPOSITIONS, INVERSES, AND COMBINATIONS OF FUNCTIONS have been answered, more than 26281 students have viewed full stepbystep solutions from this chapter.

Blocking
A feature of some experimental designs that controls for potential differences between subject groups by applying treatments randomly within homogeneous blocks of subjects

Categorical variable
In statistics, a nonnumerical variable such as gender or hair color. Numerical variables like zip codes, in which the numbers have no quantitative significance, are also considered to be categorical.

Conditional probability
The probability of an event A given that an event B has already occurred

Derivative of ƒ
The function defined by ƒ'(x) = limh:0ƒ(x + h)  ƒ(x)h for all of x where the limit exists

Equilibrium price
See Equilibrium point.

Firstdegree equation in x , y, and z
An equation that can be written in the form.

Horizontal line
y = b.

Inequality symbol or
<,>,<,>.

Linear regression equation
Equation of a linear regression line

Linear regression line
The line for which the sum of the squares of the residuals is the smallest possible

Multiplication principle of probability
If A and B are independent events, then P(A and B) = P(A) # P(B). If Adepends on B, then P(A and B) = P(AB) # P(B)

nth root
See Principal nth root

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

Polar coordinates
The numbers (r, ?) that determine a point’s location in a polar coordinate system. The number r is the directed distance and ? is the directed angle

Positive linear correlation
See Linear correlation.

Probability distribution
The collection of probabilities of outcomes in a sample space assigned by a probability function.

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

Right angle
A 90° angle.

Root of an equation
A solution.

Standard representation of a vector
A representative arrow with its initial point at the origin