 9.2.1: Determine whether each function is a onetoone function. If it is ...
 9.2.2: Determine whether each function is a onetoone function. If it is ...
 9.2.3: Determine whether each function is a onetoone function. If it is ...
 9.2.4: Determine whether each function is a onetoone function. If it is ...
 9.2.5: Determine whether each function is a onetoone function. If it is ...
 9.2.6: Determine whether each function is a onetoone function. If it is ...
 9.2.7: Month of 2009 (Input) July August September October November December
 9.2.8: State (Input) Texas Massachusetts Nevada Idaho WisconsinNumber of T...
 9.2.9: State (Input) California Alaska Indiana Louisiana New Mexico OhioRa...
 9.2.10: Shape (Input) Triangle Pentagon Quadrilateral Hexagon DecagonNumber...
 9.2.11: Given the onetoone function f 1x2 = x3 + 2, find the following. [...
 9.2.12: Given the onetoone function f 1x2 = x3 + 2, find the following. [...
 9.2.13: Given the onetoone function f 1x2 = x3 + 2, find the following. [...
 9.2.14: Given the onetoone function f 1x2 = x3 + 2, find the following. [...
 9.2.15: Determine whether the graph of each function is the graph of a one...
 9.2.16: Determine whether the graph of each function is the graph of a one...
 9.2.17: Determine whether the graph of each function is the graph of a one...
 9.2.18: Determine whether the graph of each function is the graph of a one...
 9.2.19: Determine whether the graph of each function is the graph of a one...
 9.2.20: Determine whether the graph of each function is the graph of a one...
 9.2.21: Determine whether the graph of each function is the graph of a one...
 9.2.22: Determine whether the graph of each function is the graph of a one...
 9.2.23: Each of the following functions is onetoone. Find the inverse of ...
 9.2.24: Each of the following functions is onetoone. Find the inverse of ...
 9.2.25: Each of the following functions is onetoone. Find the inverse of ...
 9.2.26: Each of the following functions is onetoone. Find the inverse of ...
 9.2.27: Each of the following functions is onetoone. Find the inverse of ...
 9.2.28: Each of the following functions is onetoone. Find the inverse of ...
 9.2.29: Each of the following functions is onetoone. Find the inverse of ...
 9.2.30: Each of the following functions is onetoone. Find the inverse of ...
 9.2.31: Find the inverse of each onetoone function. See Examples 4 and 5....
 9.2.32: Find the inverse of each onetoone function. See Examples 4 and 5....
 9.2.33: Find the inverse of each onetoone function. See Examples 4 and 5....
 9.2.34: Find the inverse of each onetoone function. See Examples 4 and 5....
 9.2.35: Find the inverse of each onetoone function. See Examples 4 and 5....
 9.2.36: Find the inverse of each onetoone function. See Examples 4 and 5....
 9.2.37: Find the inverse of each onetoone function. See Examples 4 and 5....
 9.2.38: Find the inverse of each onetoone function. See Examples 4 and 5....
 9.2.39: Find the inverse of each onetoone function. See Examples 4 and 5....
 9.2.40: Find the inverse of each onetoone function. See Examples 4 and 5....
 9.2.41: Graph the inverse of each function on the same set of axes. See Exa...
 9.2.42: Graph the inverse of each function on the same set of axes. See Exa...
 9.2.43: Graph the inverse of each function on the same set of axes. See Exa...
 9.2.44: Graph the inverse of each function on the same set of axes. See Exa...
 9.2.45: Graph the inverse of each function on the same set of axes. See Exa...
 9.2.46: Graph the inverse of each function on the same set of axes. See Exa...
 9.2.47: Solve. See Example 7.If f 1x2 = 2x + 1, show that f 11x2 = x  12
 9.2.48: Solve. See Example 7.If f 1x2 = 3x  10, show that f 11x2 = x + 103
 9.2.49: Solve. See Example 7.If f 1x2 = x3 + 6, show that f 11x2 = 23 x  6.
 9.2.50: Solve. See Example 7.If f 1x2 = x3  5, show that f 11x2 = 23 x + 5.
 9.2.51: Evaluate each of the following. See Section 7.2.251/2
 9.2.52: Evaluate each of the following. See Section 7.2.491/2
 9.2.53: Evaluate each of the following. See Section 7.2.163/4
 9.2.54: Evaluate each of the following. See Section 7.2.272/3
 9.2.55: Evaluate each of the following. See Section 7.2.93/2
 9.2.56: Evaluate each of the following. See Section 7.2.813/4
 9.2.57: If f 1x2 = 3x , find the following. In Exercises 59 and 60, give an...
 9.2.58: If f 1x2 = 3x , find the following. In Exercises 59 and 60, give an...
 9.2.59: If f 1x2 = 3x , find the following. In Exercises 59 and 60, give an...
 9.2.60: If f 1x2 = 3x , find the following. In Exercises 59 and 60, give an...
 9.2.61: Solve. See the Concept Check in this section.Suppose that f is a on...
 9.2.62: Solve. See the Concept Check in this section.Suppose that F is a on...
 9.2.63: For Exercises 63 and 64,a. Write the ordered pairs for f(x) whose p...
 9.2.64: For Exercises 63 and 64,a. Write the ordered pairs for f(x) whose p...
 9.2.65: If you are given the graph of a function, describe how you can tell...
 9.2.66: Describe the appearance of the graphs of a function and its inverse.
 9.2.67: Find the inverse of each given onetoone function. Then use a grap...
 9.2.68: Find the inverse of each given onetoone function. Then use a grap...
 9.2.69: Find the inverse of each given onetoone function. Then use a grap...
 9.2.70: Find the inverse of each given onetoone function. Then use a grap...
Solutions for Chapter 9.2: Inverse Functions
Full solutions for Intermediate Algebra  6th Edition
ISBN: 9780321785046
Solutions for Chapter 9.2: Inverse Functions
Get Full SolutionsIntermediate Algebra was written by and is associated to the ISBN: 9780321785046. Since 70 problems in chapter 9.2: Inverse Functions have been answered, more than 63016 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Intermediate Algebra, edition: 6. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 9.2: Inverse Functions includes 70 full stepbystep solutions.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

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).

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

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

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.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

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.

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.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

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

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

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

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.