 2.7.a: Let represent the retail price of an item (in dollars), and let rep...
 2.7.1: If the composite functions and both equal then the function is the ...
 2.7.b: Let represent the temperature in degrees Celsius, and let represent...
 2.7.2: The inverse function of is denoted by ________.
 2.7.3: The domain of is the ________ of and the ________ of is the range
 2.7.4: The graphs of and are reflections of each other in the line ________.
 2.7.5: A function is ________ if each value of the dependent variable corr...
 2.7.6: A graphical test for the existence of an inverse function of is cal...
 2.7.7: f x 6x
 2.7.8: f x 1 3 f x 6x x
 2.7.9: f x x 9
 2.7.10: f x x 4
 2.7.11: f x 3x 1
 2.7.12: f x x 1 5 f
 2.7.13: f x 3 x f
 2.7.14: f x x5 f
 2.7.15: 1 234 2 1 3 4 y
 2.7.16: x 1 2 3 456 2 1 3 4 5 6 y
 2.7.17: 4 2 4 1 3 y
 2.7.18: 3 3 y
 2.7.19: 2x 6 7 f
 2.7.20: f x g x 4x 9
 2.7.21: f x x x 5 3
 2.7.22: f x 2x
 2.7.23: x 2 f
 2.7.24: f x x 5, g x x 5
 2.7.25: x 1 7 f x
 2.7.26: g x 3 x 4 f x
 2.7.27: f x 8x
 2.7.28: g x 1 x f
 2.7.29: f x x 4, 2
 2.7.30: f x 1 x 1 x 3,
 2.7.31: f x 9 x x 0, g x 9 x, x 9 2,
 2.7.32:
 2.7.33: g x 5x 1 x 1 f x
 2.7.34: 2x 3 x 1 f x
 2.7.35: x 1 0 1 2 3 4 f x 2 121 2 6 x 3
 2.7.36: x 3 2 1 0 2 3 f x 10 6 4 1 3 10 Sect
 2.7.37: x 2 1 0 1 2 3 f x 2 0 2468 x
 2.7.38: x 3 2 1 0 1 2 f x 10 7 4 1 2 5 x 1 0
 2.7.39: 246 2 2 6 4 y
 2.7.40: 2 4 2 2 6
 2.7.41: 2 2 2 y
 2.7.42: 6 2 2 4 y
 2.7.43: g x 4 x 6
 2.7.44: f x 10
 2.7.45: h x x 4 x 4 f
 2.7.46: g x x 53
 2.7.47: f x 2x16 x2 g
 2.7.48: f x 1 8 x 22 1
 2.7.49: f x 2x 3 f
 2.7.50: f x 3x 1
 2.7.51: f x x 3 1 5 2
 2.7.52: f x x f x x 3 1 5
 2.7.53: f x 4 x 0 x 2 2
 2.7.54: f x x x 0
 2.7.55: f x 4 x
 2.7.56: f x 2 x
 2.7.57: f x x 1 x 2
 2.7.58: f x x 3 x 2 f
 2.7.59: f x 3 x 1 f
 2.7.60: f x x3 5
 2.7.61: f x 6x 4 4x 5
 2.7.62: f x 8x 4 2x 6 f
 2.7.63: f x x4
 2.7.64: f x 1 x 2
 2.7.65: g x f x 3x 5 x 8
 2.7.66: f x 3x 5
 2.7.67: p x 4
 2.7.68: f x 3x 4 5
 2.7.69: f x x 3 x 3 2
 2.7.70: q x x 52 f
 2.7.71: f x x 3, 6 x, x < 0 x 0
 2.7.72: f x x, x2 3x, x 0 x > 0 f
 2.7.73: h x f x x 2 , x 2 4 x2 f
 2.7.74: f x x 2 , x 2
 2.7.75: f x 2x 3 7
 2.7.76: f x x 2 h
 2.7.77: f x x 22
 2.7.78: f x 1 x 4 f
 2.7.79: f x x 2
 2.7.80: f x x 5 f
 2.7.81: f x x 62
 2.7.82: f x x 42 f
 2.7.83: f x 2x 2 1 2 5 f
 2.7.84: f x 1 2 x f x 2x 2 1 2
 2.7.85: f x x 4 1 x
 2.7.86: f x f x x 4 1 x 1 2 f x
 2.7.87: f 3 1 g1 1 gx
 2.7.88: g1 f 1 f 3 1
 2.7.89: f 4 1 f 1 6 g
 2.7.90: g1 g1 f 4 1
 2.7.91: f g1
 2.7.92: g1 f 1 f
 2.7.93: g1 f 1 g
 2.7.94: f 1 g1 g1
 2.7.95: f g1 f
 2.7.96: g f 1 f
 2.7.97: SHOE SIZES The table shows mens shoe sizes in the United States and...
 2.7.98: SHOE SIZES The table shows womens shoe sizes in the United States a...
 2.7.99: LCD TVS The sales S (in millions of dollars) of LCD televisions in ...
 2.7.100: POPULATION The projected populations (in millions of people) in the...
 2.7.101: HOURLY WAGE Your wage is $10.00 per hour plus $0.75 for each unit p...
 2.7.102: DIESEL MECHANICS The function given by approximates the exhaust tem...
 2.7.103: If is an even function, then exists.
 2.7.104: If the inverse function of exists and the graph of has a intercept...
 2.7.105: PROOF Prove that if and are onetoone functions, then
 2.7.106: PROOF Prove that if is a onetoone odd function, then is an odd fu...
 2.7.107: f 2 8 6 2 6 8 y
 2.7.108: 4 2 4 f 4 y
 2.7.109: The number of miles a marathon runner has completed in terms of the...
 2.7.110: The population of South Carolina in terms of the year from 1960 thr...
 2.7.111: The depth of the tide at a beach in terms of the time over a 24hou...
 2.7.112: The height in inches of a human born in the year 2000 in terms of h...
 2.7.113: THINK ABOUT IT The function given by has an inverse function, and
 2.7.114: THINK ABOUT IT Consider the functions given by and Evaluate and for...
 2.7.115: THINK ABOUT IT Restrict the domain of to Use a graphing utility to ...
 2.7.116: CAPSTONE D
Solutions for Chapter 2.7: Inverse Functions
Full solutions for Algebra and Trigonometry  8th Edition
ISBN: 9781439048474
Solutions for Chapter 2.7: Inverse Functions
Get Full SolutionsThis textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 8. Since 118 problems in chapter 2.7: Inverse Functions have been answered, more than 31812 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Algebra and Trigonometry was written by and is associated to the ISBN: 9781439048474. Chapter 2.7: Inverse Functions includes 118 full stepbystep solutions.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

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

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

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

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

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

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

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

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

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

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.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).