 101.10.1.1: In Exercises 12, find and simplify for f(x)=2x and g(x) = x x + 1f(...
 101.10.1.2: In Exercises 12, find and simplify for f(x)=2x and g(x) = x x + 1g(...
 101.10.1.3: Let f(x) = sin 4x and g(x) = x. Find formulas for f(g(x)) and g(f(x)).
 101.10.1.4: Let m(x)= 3+ x2 and n(x) = tan x. Find formulas for m(n(x)) and n(m...
 101.10.1.5: Find a formula in terms of x for the function w(x) = p(p(x)), where...
 101.10.1.6: . Use Table 10.2 to construct a table of values for r(x) = p(q(x)).
 101.10.1.7: Let p and q be the functions in Exercise 6. Construct a table of va...
 101.10.1.8: In Exercises 813, let f(x)=3x2, g(x)=9x 2, m(x) = 4x, and r(x) = 3x...
 101.10.1.9: In Exercises 813, let f(x)=3x2, g(x)=9x 2, m(x) = 4x, and r(x) = 3x...
 101.10.1.10: In Exercises 813, let f(x)=3x2, g(x)=9x 2, m(x) = 4x, and r(x) = 3x...
 101.10.1.11: In Exercises 813, let f(x)=3x2, g(x)=9x 2, m(x) = 4x, and r(x) = 3x...
 101.10.1.12: In Exercises 813, let f(x)=3x2, g(x)=9x 2, m(x) = 4x, and r(x) = 3x...
 101.10.1.13: In Exercises 813, let f(x)=3x2, g(x)=9x 2, m(x) = 4x, and r(x) = 3x...
 101.10.1.14: In Exercises 1418, identify the function f(x).h(x) = ef(x) = esin x
 101.10.1.15: In Exercises 1418, identify the function f(x).j(x) = f(x) = ln(x2 + 4)
 101.10.1.16: In Exercises 1418, identify the function f(x).k(x) = sin(f(x)) = si...
 101.10.1.17: In Exercises 1418, identify the function f(x).l(x)=(f(x))2 = cos2 2x
 101.10.1.18: In Exercises 1418, identify the function f(x).l(x)=(f(x))2 = cos2 2x
 101.10.1.19: In 1922, give a practical interpretation in words of the function.f...
 101.10.1.20: In 1922, give a practical interpretation in words of the function.k...
 101.10.1.21: In 1922, give a practical interpretation in words of the function.R...
 101.10.1.22: In 1922, give a practical interpretation in words of the function.t...
 101.10.1.23: Suppose u(v(x)) = 1 x2 1 and v(u(x)) = 1 (x 1)2 . Find possible for...
 101.10.1.24: In 2427, suppose that f(x) = g(h(x)). Find possible formulas for g(...
 101.10.1.25: In 2427, suppose that f(x) = g(h(x)). Find possible formulas for g(...
 101.10.1.26: In 2427, suppose that f(x) = g(h(x)). Find possible formulas for g(...
 101.10.1.27: In 2427, suppose that f(x) = g(h(x)). Find possible formulas for g(...
 101.10.1.28: Complete Table 10.3 given that h(x) = f(g(x)).
 101.10.1.29: Complete the table given h(x) = g(f(x)).
 101.10.1.30: Complete Table 10.4 given that w(t) = v(u(t)).
 101.10.1.31: In 3133, let x > 0 and k(x) = ex. Find a possible formula for f(x)....
 101.10.1.32: In 3133, let x > 0 and k(x) = ex. Find a possible formula for f(x)....
 101.10.1.33: In 3133, let x > 0 and k(x) = ex. Find a possible formula for f(x)....
 101.10.1.34: In 3437, find a simplified formula for the difference quotient f(x ...
 101.10.1.35: In 3437, find a simplified formula for the difference quotient f(x ...
 101.10.1.36: In 3437, find a simplified formula for the difference quotient f(x ...
 101.10.1.37: In 3437, find a simplified formula for the difference quotient f(x ...
 101.10.1.38: Using Figure 10.2, estimate the following: (a) f(g(2)) (b) g(f(2))(...
 101.10.1.39: Use Figure 10.3 to calculate the following: (a) f(f(1)) (b) g(g(1))...
 101.10.1.40: Use Figure 10.3 to find all solutions to the equations: (a) f(g(x))...
 101.10.1.41: Let f(x) and g(x) be the functions in Figure 10.3. (a) Graph the fu...
 101.10.1.42: In 4245, use the information from Figures 10.4 and 10.5 to graph th...
 101.10.1.43: In 4245, use the information from Figures 10.4 and 10.5 to graph th...
 101.10.1.44: In 4245, use the information from Figures 10.4 and 10.5 to graph th...
 101.10.1.45: In 4245, use the information from Figures 10.4 and 10.5 to graph th...
 101.10.1.46: Find f(f(1)) for f(x) = 2 if x 0 3x + 1 if 0
 101.10.1.47: If s(x)=5+ 1 x + 5 + x, k(x) = x + 5, and s(x) = v(k(x)), what is v...
 101.10.1.48: Let f(x) = 12 4x, g(x)=1/x, and h(x) = x 4. Find the domain of the ...
 101.10.1.49: Decompose the functions in 4954 into u(v(x)) for given u or v.y = 1...
 101.10.1.50: Decompose the functions in 4954 into u(v(x)) for given u or v.y = e...
 101.10.1.51: Decompose the functions in 4954 into u(v(x)) for given u or v.y = 1...
 101.10.1.52: Decompose the functions in 4954 into u(v(x)) for given u or v.y = 2...
 101.10.1.53: Decompose the functions in 4954 into u(v(x)) for given u or v.y = s...
 101.10.1.54: Decompose the functions in 4954 into u(v(x)) for given u or v.y = e...
 101.10.1.55: (a) Use Table 10.5 and Figure 10.6 to calculate: (i) f(g(4)) (ii) g...
 101.10.1.56: You have two money machines, both of which increase any money inser...
 101.10.1.57: Let p(t) = 10(0.01)t and q(t) = log t 2. Solve the equation q(p(t))...
 101.10.1.58: Let f(t) = sin t and g(t)=3t/4. Solve the equation f(g(t)) = 1 for ...
 101.10.1.59: Let f(x) = x and g(x) = x2. Calculate the domain of f(g(x)) and the...
 101.10.1.60: The graphs for y = f(x) and y = g(x) are shown in Figure 10.7. (a) ...
 101.10.1.61: Letting r(x)=3x3 4x2 , find q(x) given that q(r(x)) = 8x3 16x2 .
 101.10.1.62: In 6263, find a simplified formula for g given that f(x) = x + 1 x ...
 101.10.1.63: In 6263, find a simplified formula for g given that f(x) = x + 1 x ...
 101.10.1.64: Which of the following statements must be true in order for the poi...
 101.10.1.65: Which of the following statements must be true in order for h(x) = ...
Solutions for Chapter 101: COMPOSITION OF FUNCTIONS
Full solutions for Functions Modeling Change: A Preparation for Calculus  4th Edition
ISBN: 9780470484753
Solutions for Chapter 101: COMPOSITION OF FUNCTIONS
Get Full SolutionsFunctions Modeling Change: A Preparation for Calculus was written by and is associated to the ISBN: 9780470484753. This 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 101: COMPOSITION OF FUNCTIONS includes 65 full stepbystep solutions. Since 65 problems in chapter 101: COMPOSITION OF FUNCTIONS have been answered, more than 26120 students have viewed full stepbystep solutions from this chapter.

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

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

Complex number
An expression a + bi, where a (the real part) and b (the imaginary part) are real numbers

Conjugate axis of a hyperbola
The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint

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

Difference of two vectors
<u1, u2>  <v1, v2> = <u1  v1, u2  v2> or <u1, u2, u3>  <v1, v2, v3> = <u1  v1, u2  v2, u3  v3>

Division
a b = aa 1 b b, b Z 0

Imaginary axis
See Complex plane.

Inverse cosecant function
The function y = csc1 x

Lower bound of f
Any number b for which b < ƒ(x) for all x in the domain of ƒ

Mathematical induction
A process for proving that a statement is true for all natural numbers n by showing that it is true for n = 1 (the anchor) and that, if it is true for n = k, then it must be true for n = k + 1 (the inductive step)

Matrix element
Any of the real numbers in a matrix

Pythagorean
Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2

Quadratic function
A function that can be written in the form ƒ(x) = ax 2 + bx + c, where a, b, and c are real numbers, and a ? 0.

Relevant domain
The portion of the domain applicable to the situation being modeled.

Root of an equation
A solution.

Secant
The function y = sec x.

Solution of an equation or inequality
A value of the variable (or values of the variables) for which the equation or inequality is true

Spiral of Archimedes
The graph of the polar curve.

Zero matrix
A matrix consisting entirely of zeros.