 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 16424 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.

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

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.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Spectrum of A = the set of eigenvalues {A I, ... , An}.
Spectral radius = max of IAi I.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

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.
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