 3.7.1: Describe why the horizontal line test is an effective way to determ...
 3.7.2: Why do we restrict the domain of the function f(x) = x2 to find the...
 3.7.3: Can a function be its own inverse? Explain.
 3.7.4: Are onetoone functions either always increasing or always decreas...
 3.7.5: How do you find the inverse of a function algebraically?
 3.7.6: Show that the function f(x) = a x is its own inverse for all real n...
 3.7.7: For the following exercises, find f 1 (x) for each function. f (x) ...
 3.7.8: For the following exercises, find f 1 (x) for each function. f (x) ...
 3.7.9: For the following exercises, find f 1 (x) for each function. f (x) ...
 3.7.10: For the following exercises, find f 1 (x) for each function. f (x) ...
 3.7.11: For the following exercises, find f 1 (x) for each function.. f (x)...
 3.7.12: For the following exercises, find f 1 (x) for each function. f(x) =...
 3.7.13: For the following exercises, find a domain on which each function f...
 3.7.14: For the following exercises, find a domain on which each function f...
 3.7.15: For the following exercises, find a domain on which each function f...
 3.7.16: Given f(x) = x 3 5 and g(x) = _____ 2x 1 x : a. Find f(g(x)) and g ...
 3.7.17: For the following exercises, use function composition to verify tha...
 3.7.18: For the following exercises, use function composition to verify tha...
 3.7.19: For the following exercises, use a graphing utility to determine wh...
 3.7.20: For the following exercises, use a graphing utility to determine wh...
 3.7.21: For the following exercises, use a graphing utility to determine wh...
 3.7.22: For the following exercises, use a graphing utility to determine wh...
 3.7.23: For the following exercises, determine whether the graph represents...
 3.7.24: For the following exercises, determine whether the graph represents...
 3.7.25: For the following exercises, use the graph of f shown in Figure 11....
 3.7.26: For the following exercises, use the graph of f shown in Figure 11....
 3.7.27: For the following exercises, use the graph of f shown in Figure 11....
 3.7.28: For the following exercises, use the graph of f shown in Figure 11....
 3.7.29: For the following exercises, use the graph of the onetoone functi...
 3.7.30: For the following exercises, use the graph of the onetoone functi...
 3.7.31: For the following exercises, use the graph of the onetoone functi...
 3.7.32: For the following exercises, use the graph of the onetoone functi...
 3.7.33: For the following exercises, evaluate or solve, assuming that the f...
 3.7.34: For the following exercises, evaluate or solve, assuming that the f...
 3.7.35: For the following exercises, evaluate or solve, assuming that the f...
 3.7.36: For the following exercises, evaluate or solve, assuming that the f...
 3.7.37: For the following exercises, use the values listed in Table 6 to ev...
 3.7.38: For the following exercises, use the values listed in Table 6 to ev...
 3.7.39: For the following exercises, use the values listed in Table 6 to ev...
 3.7.40: For the following exercises, use the values listed in Table 6 to ev...
 3.7.41: Use the tabular representation of f in Table 7 to create a table fo...
 3.7.42: For the following exercises, find the inverse function. Then, graph...
 3.7.43: For the following exercises, find the inverse function. Then, graph...
 3.7.44: Find the inverse function of f(x) = _1 x 1 . Use a graphing utility...
 3.7.45: To convert from x degrees Celsius to y degrees Fahrenheit, we use t...
 3.7.46: The circumference C of a circle is a function of its radius given b...
 3.7.47: A car travels at a constant speed of 50 miles per hour. The distanc...
Solutions for Chapter 3.7: INVERSE FUNCTIONS
Full solutions for College Algebra  1st Edition
ISBN: 9781938168383
Solutions for Chapter 3.7: INVERSE FUNCTIONS
Get Full SolutionsThis textbook survival guide was created for the textbook: College Algebra, edition: 1. Chapter 3.7: INVERSE FUNCTIONS includes 47 full stepbystep solutions. Since 47 problems in chapter 3.7: INVERSE FUNCTIONS have been answered, more than 32126 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. College Algebra was written by and is associated to the ISBN: 9781938168383.

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).

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].

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

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

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.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

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.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = 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.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

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.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

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

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

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

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.