 9.2.1: The notation f g, called the ____________ of the function f with g,...
 9.2.2: I find (f g)(x) by replacing each occurrence of x in the equation f...
 9.2.3: The notation g f, called the ____________ of the function g with f,...
 9.2.4: I find (g f)(x) by replacing each occurrence of x in the equation f...
 9.2.5: True or false: f g is the same function as g f. ____________
 9.2.6: True or false: f(g(x)) = f(x) # g(x) ____________
 9.2.7: The notation f 1 means the ____________ of the function f
 9.2.8: If the function g is the inverse of the function f, then f(g(x)) = ...
 9.2.9: A function f has an inverse that is a function if there is no _____...
 9.2.10: The graph of f 1 is a reflection of the graph of f about the line ...
 9.2.11: In Exercises 114, find a. (f g)(x); b. (g f)(x); c. (f g)(2).f(x) =...
 9.2.12: In Exercises 114, find a. (f g)(x); b. (g f)(x); c. (f g)(2).f(x) =...
 9.2.13: In Exercises 114, find a. (f g)(x); b. (g f)(x); c. (f g)(2).f(x) =...
 9.2.14: In Exercises 114, find a. (f g)(x); b. (g f)(x); c. (f g)(2).f(x) =...
 9.2.15: In Exercises 1524, find f(g(x)) and g(f(x)) and determine whether e...
 9.2.16: In Exercises 1524, find f(g(x)) and g(f(x)) and determine whether e...
 9.2.17: In Exercises 1524, find f(g(x)) and g(f(x)) and determine whether e...
 9.2.18: In Exercises 1524, find f(g(x)) and g(f(x)) and determine whether e...
 9.2.19: In Exercises 1524, find f(g(x)) and g(f(x)) and determine whether e...
 9.2.20: In Exercises 1524, find f(g(x)) and g(f(x)) and determine whether e...
 9.2.21: In Exercises 1524, find f(g(x)) and g(f(x)) and determine whether e...
 9.2.22: In Exercises 1524, find f(g(x)) and g(f(x)) and determine whether e...
 9.2.23: In Exercises 1524, find f(g(x)) and g(f(x)) and determine whether e...
 9.2.24: In Exercises 1524, find f(g(x)) and g(f(x)) and determine whether e...
 9.2.25: The functions in Exercises 2544 are all onetoone. For each functi...
 9.2.26: The functions in Exercises 2544 are all onetoone. For each functi...
 9.2.27: The functions in Exercises 2544 are all onetoone. For each functi...
 9.2.28: The functions in Exercises 2544 are all onetoone. For each functi...
 9.2.29: The functions in Exercises 2544 are all onetoone. For each functi...
 9.2.30: The functions in Exercises 2544 are all onetoone. For each functi...
 9.2.31: The functions in Exercises 2544 are all onetoone. For each functi...
 9.2.32: The functions in Exercises 2544 are all onetoone. For each functi...
 9.2.33: The functions in Exercises 2544 are all onetoone. For each functi...
 9.2.34: The functions in Exercises 2544 are all onetoone. For each functi...
 9.2.35: The functions in Exercises 2544 are all onetoone. For each functi...
 9.2.36: The functions in Exercises 2544 are all onetoone. For each functi...
 9.2.37: The functions in Exercises 2544 are all onetoone. For each functi...
 9.2.38: The functions in Exercises 2544 are all onetoone. For each functi...
 9.2.39: The functions in Exercises 2544 are all onetoone. For each functi...
 9.2.40: The functions in Exercises 2544 are all onetoone. For each functi...
 9.2.41: The functions in Exercises 2544 are all onetoone. For each functi...
 9.2.42: The functions in Exercises 2544 are all onetoone. For each functi...
 9.2.43: The functions in Exercises 2544 are all onetoone. For each functi...
 9.2.44: The functions in Exercises 2544 are all onetoone. For each functi...
 9.2.45: Which graphs in Exercises 4550 represent functions that have invers...
 9.2.46: Which graphs in Exercises 4550 represent functions that have invers...
 9.2.47: Which graphs in Exercises 4550 represent functions that have invers...
 9.2.48: Which graphs in Exercises 4550 represent functions that have invers...
 9.2.49: Which graphs in Exercises 4550 represent functions that have invers...
 9.2.50: Which graphs in Exercises 4550 represent functions that have invers...
 9.2.51: In Exercises 5154, use the graph of f to draw the graph of its inve...
 9.2.52: In Exercises 5154, use the graph of f to draw the graph of its inve...
 9.2.53: In Exercises 5154, use the graph of f to draw the graph of its inve...
 9.2.54: In Exercises 5154, use the graph of f to draw the graph of its inve...
 9.2.55: In Exercises 5560, f and g are defined by the following tables.Use ...
 9.2.56: In Exercises 5560, f and g are defined by the following tables.Use ...
 9.2.57: In Exercises 5560, f and g are defined by the following tables.Use ...
 9.2.58: In Exercises 5560, f and g are defined by the following tables.Use ...
 9.2.59: In Exercises 5560, f and g are defined by the following tables.Use ...
 9.2.60: In Exercises 5560, f and g are defined by the following tables.Use ...
 9.2.61: In Exercises 6164, use the graphs of f and g to evaluate each compo...
 9.2.62: In Exercises 6164, use the graphs of f and g to evaluate each compo...
 9.2.63: In Exercises 6164, use the graphs of f and g to evaluate each compo...
 9.2.64: In Exercises 6164, use the graphs of f and g to evaluate each compo...
 9.2.65: In Exercises 6570, let f(x) = 2x  5 g(x) = 4x  1 h(x) = x2 + x + ...
 9.2.66: In Exercises 6570, let f(x) = 2x  5 g(x) = 4x  1 h(x) = x2 + x + ...
 9.2.67: In Exercises 6570, let f(x) = 2x  5 g(x) = 4x  1 h(x) = x2 + x + ...
 9.2.68: In Exercises 6570, let f(x) = 2x  5 g(x) = 4x  1 h(x) = x2 + x + ...
 9.2.69: In Exercises 6570, let f(x) = 2x  5 g(x) = 4x  1 h(x) = x2 + x + ...
 9.2.70: In Exercises 6570, let f(x) = 2x  5 g(x) = 4x  1 h(x) = x2 + x + ...
 9.2.71: The regular price of a computer is x dollars. Let f(x) = x  400 an...
 9.2.72: The regular price of a pair of jeans is x dollars. Let f(x) = x  5...
 9.2.73: Way to Go Holland was the first country to establish an official bi...
 9.2.74: Way to Go Holland was the first country to establish an official bi...
 9.2.75: The graph represents the probability that two people in the same ro...
 9.2.76: A study of 900 working women in Texas showed that their feelings ch...
 9.2.77: The formula y = f(x) = 9 5 x + 32 is used to convert from x degrees...
 9.2.78: Describe a procedure for finding (f g)(x).
 9.2.79: Explain how to determine if two functions are inverses of each other.
 9.2.80: Describe how to find the inverse of a onetoone function.
 9.2.81: What is the horizontal line test and what does it indicate?
 9.2.82: Describe how to use the graph of a onetoone function to draw the ...
 9.2.83: How can a graphing utility be used to visually determine if two fun...
 9.2.84: n Exercises 8491, use a graphing utility to graph each function. Us...
 9.2.85: n Exercises 8491, use a graphing utility to graph each function. Us...
 9.2.86: n Exercises 8491, use a graphing utility to graph each function. Us...
 9.2.87: n Exercises 8491, use a graphing utility to graph each function. Us...
 9.2.88: n Exercises 8491, use a graphing utility to graph each function. Us...
 9.2.89: n Exercises 8491, use a graphing utility to graph each function. Us...
 9.2.90: n Exercises 8491, use a graphing utility to graph each function. Us...
 9.2.91: n Exercises 8491, use a graphing utility to graph each function. Us...
 9.2.92: In Exercises 9294, use a graphing utility to graph f and g in the s...
 9.2.93: In Exercises 9294, use a graphing utility to graph f and g in the s...
 9.2.94: In Exercises 9294, use a graphing utility to graph f and g in the s...
 9.2.95: Make Sense? In Exercises 9598, determine whether each statement mak...
 9.2.96: Make Sense? In Exercises 9598, determine whether each statement mak...
 9.2.97: Make Sense? In Exercises 9598, determine whether each statement mak...
 9.2.98: Make Sense? In Exercises 9598, determine whether each statement mak...
 9.2.99: In Exercises 99102, determine whether each statement is true or fal...
 9.2.100: In Exercises 99102, determine whether each statement is true or fal...
 9.2.101: In Exercises 99102, determine whether each statement is true or fal...
 9.2.102: In Exercises 99102, determine whether each statement is true or fal...
 9.2.103: If h(x) = 23x2 + 5, find functions f and g so that h(x) = (f g)(x).
 9.2.104: If f(x) = 3x and g(x) = x + 5, find (f g) 1 (x) and (g1 f 1 )(x).
 9.2.105: Show that f(x) = 3x  2 5x  3 is its own inverse.
 9.2.106: Consider the two functions defined by f(x) = m1x + b1 and g(x) = m2...
 9.2.107: Divide and write the quotient in scientific notation: 4.3 * 105 8.6...
 9.2.108: Graph: f(x) = x2  4x + 3. (Section 8.3, Example 4)
 9.2.109: Solve: 2x + 4  2x  1 = 1. (Section 7.6, Example 4)
 9.2.110: Exercises 110112 will help you prepare for the material covered in ...
 9.2.111: Exercises 110112 will help you prepare for the material covered in ...
 9.2.112: Exercises 110112 will help you prepare for the material covered in ...
Solutions for Chapter 9.2: Composite and Inverse Functions
Full solutions for Intermediate Algebra for College Students  6th Edition
ISBN: 9780321758934
Solutions for Chapter 9.2: Composite and Inverse Functions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 9.2: Composite and Inverse Functions includes 112 full stepbystep solutions. This textbook survival guide was created for the textbook: Intermediate Algebra for College Students, edition: 6. Since 112 problems in chapter 9.2: Composite and Inverse Functions have been answered, more than 38558 students have viewed full stepbystep solutions from this chapter. Intermediate Algebra for College Students was written by and is associated to the ISBN: 9780321758934.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Column space C (A) =
space of all combinations of the columns of A.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.