 2.7.1: Fill in the blanks. If the composite functions and both equal then ...
 2.7.2: Fill in the blanks. The inverse function of is denoted by ________.
 2.7.3: Fill in the blanks. The domain of is the ________ of and the ______...
 2.7.4: Fill in the blanks. The graphs of and are reflections of each other...
 2.7.5: Fill in the blanks. A function is ________ if each value of the dep...
 2.7.6: Fill in the blanks. A graphical test for the existence of an invers...
 2.7.7: In Exercises 714, find the inverse function of informally. Verify t...
 2.7.8: In Exercises 714, find the inverse function of informally. Verify t...
 2.7.9: In Exercises 714, find the inverse function of informally. Verify t...
 2.7.10: In Exercises 714, find the inverse function of informally. Verify t...
 2.7.11: In Exercises 714, find the inverse function of informally. Verify t...
 2.7.12: In Exercises 714, find the inverse function of informally. Verify t...
 2.7.13: In Exercises 714, find the inverse function of informally. Verify t...
 2.7.14: In Exercises 714, find the inverse function of informally. Verify t...
 2.7.15: In Exercises 1518, match the graph of the function with the graph o...
 2.7.16: In Exercises 1518, match the graph of the function with the graph o...
 2.7.17: In Exercises 1518, match the graph of the function with the graph o...
 2.7.18: In Exercises 1518, match the graph of the function with the graph o...
 2.7.19: In Exercises 1922, verify that and are inverse functions.
 2.7.20: In Exercises 1922, verify that and are inverse functions.
 2.7.21: In Exercises 1922, verify that and are inverse functions.
 2.7.22: In Exercises 1922, verify that and are inverse functions.
 2.7.23: In Exercises 2334, show that and are inverse functions (a) algebrai...
 2.7.24: In Exercises 2334, show that and are inverse functions (a) algebrai...
 2.7.25: In Exercises 2334, show that and are inverse functions (a) algebrai...
 2.7.26: In Exercises 2334, show that and are inverse functions (a) algebrai...
 2.7.27: In Exercises 2334, show that and are inverse functions (a) algebrai...
 2.7.28: In Exercises 2334, show that and are inverse functions (a) algebrai...
 2.7.29: In Exercises 2334, show that and are inverse functions (a) algebrai...
 2.7.30: In Exercises 2334, show that and are inverse functions (a) algebrai...
 2.7.31: In Exercises 2334, show that and are inverse functions (a) algebrai...
 2.7.32: In Exercises 2334, show that and are inverse functions (a) algebrai...
 2.7.33: In Exercises 2334, show that and are inverse functions (a) algebrai...
 2.7.34: In Exercises 2334, show that and are inverse functions (a) algebrai...
 2.7.35: In Exercises 35 and 36, does the function have an inverse function?
 2.7.36: In Exercises 35 and 36, does the function have an inverse function?
 2.7.37: In Exercises 37 and 38, use the table of values for to complete a t...
 2.7.38: In Exercises 37 and 38, use the table of values for to complete a t...
 2.7.39: In Exercises 39 42, does the function have an inverse function?
 2.7.40: In Exercises 39 42, does the function have an inverse function?
 2.7.41: In Exercises 39 42, does the function have an inverse function?
 2.7.42: In Exercises 39 42, does the function have an inverse function?
 2.7.43: In Exercises 4348, use a graphing utility to graph the function, an...
 2.7.44: In Exercises 4348, use a graphing utility to graph the function, an...
 2.7.45: In Exercises 4348, use a graphing utility to graph the function, an...
 2.7.46: In Exercises 4348, use a graphing utility to graph the function, an...
 2.7.47: In Exercises 4348, use a graphing utility to graph the function, an...
 2.7.48: In Exercises 4348, use a graphing utility to graph the function, an...
 2.7.49: In Exercises 49 62, (a) find the inverse function of (b) graph both...
 2.7.50: In Exercises 49 62, (a) find the inverse function of (b) graph both...
 2.7.51: In Exercises 49 62, (a) find the inverse function of (b) graph both...
 2.7.52: In Exercises 49 62, (a) find the inverse function of (b) graph both...
 2.7.53: In Exercises 49 62, (a) find the inverse function of (b) graph both...
 2.7.54: In Exercises 49 62, (a) find the inverse function of (b) graph both...
 2.7.55: In Exercises 49 62, (a) find the inverse function of (b) graph both...
 2.7.56: In Exercises 49 62, (a) find the inverse function of (b) graph both...
 2.7.57: In Exercises 49 62, (a) find the inverse function of (b) graph both...
 2.7.58: In Exercises 49 62, (a) find the inverse function of (b) graph both...
 2.7.59: In Exercises 49 62, (a) find the inverse function of (b) graph both...
 2.7.60: In Exercises 49 62, (a) find the inverse function of (b) graph both...
 2.7.61: In Exercises 49 62, (a) find the inverse function of (b) graph both...
 2.7.62: In Exercises 49 62, (a) find the inverse function of (b) graph both...
 2.7.63: In Exercises 6376, determine whether the function has an inverse fu...
 2.7.64: In Exercises 6376, determine whether the function has an inverse fu...
 2.7.65: In Exercises 6376, determine whether the function has an inverse fu...
 2.7.66: In Exercises 6376, determine whether the function has an inverse fu...
 2.7.67: In Exercises 6376, determine whether the function has an inverse fu...
 2.7.68: In Exercises 6376, determine whether the function has an inverse fu...
 2.7.69: In Exercises 6376, determine whether the function has an inverse fu...
 2.7.70: In Exercises 6376, determine whether the function has an inverse fu...
 2.7.71: In Exercises 6376, determine whether the function has an inverse fu...
 2.7.72: In Exercises 6376, determine whether the function has an inverse fu...
 2.7.73: In Exercises 6376, determine whether the function has an inverse fu...
 2.7.74: In Exercises 6376, determine whether the function has an inverse fu...
 2.7.75: In Exercises 6376, determine whether the function has an inverse fu...
 2.7.76: In Exercises 6376, determine whether the function has an inverse fu...
 2.7.77: THINK ABOUT IT In Exercises 77 86, restrict the domain of the funct...
 2.7.78: THINK ABOUT IT In Exercises 77 86, restrict the domain of the funct...
 2.7.79: THINK ABOUT IT In Exercises 77 86, restrict the domain of the funct...
 2.7.80: THINK ABOUT IT In Exercises 77 86, restrict the domain of the funct...
 2.7.81: THINK ABOUT IT In Exercises 77 86, restrict the domain of the funct...
 2.7.82: THINK ABOUT IT In Exercises 77 86, restrict the domain of the funct...
 2.7.83: THINK ABOUT IT In Exercises 77 86, restrict the domain of the funct...
 2.7.84: THINK ABOUT IT In Exercises 77 86, restrict the domain of the funct...
 2.7.85: THINK ABOUT IT In Exercises 77 86, restrict the domain of the funct...
 2.7.86: THINK ABOUT IT In Exercises 77 86, restrict the domain of the funct...
 2.7.87: In Exercises 87 92, use the functions given by and to find the indi...
 2.7.88: In Exercises 87 92, use the functions given by and to find the indi...
 2.7.89: In Exercises 87 92, use the functions given by and to find the indi...
 2.7.90: In Exercises 87 92, use the functions given by and to find the indi...
 2.7.91: In Exercises 87 92, use the functions given by and to find the indi...
 2.7.92: In Exercises 87 92, use the functions given by and to find the indi...
 2.7.93: In Exercises 9396, use the functions given by and to find the speci...
 2.7.94: In Exercises 9396, use the functions given by and to find the speci...
 2.7.95: In Exercises 9396, use the functions given by and to find the speci...
 2.7.96: In Exercises 9396, use the functions given by and to find the speci...
 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: In Exercises 107 and 108, use the graph of the function to create a...
 2.7.108: In Exercises 107 and 108, use the graph of the function to create a...
 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 Find
 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 Describe and correct the error.
Solutions for Chapter 2.7: INVERSE FUNCTIONS
Full solutions for College Algebra  8th Edition
ISBN: 9781439048696
Solutions for Chapter 2.7: INVERSE FUNCTIONS
Get Full SolutionsChapter 2.7: INVERSE FUNCTIONS includes 116 full stepbystep solutions. This textbook survival guide was created for the textbook: College Algebra , edition: 8. Since 116 problems in chapter 2.7: INVERSE FUNCTIONS have been answered, more than 24981 students have viewed full stepbystep solutions from this chapter. College Algebra was written by and is associated to the ISBN: 9781439048696. This expansive textbook survival guide covers the following chapters and their solutions.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

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.

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

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 .

Iterative method.
A sequence of steps intended to approach the desired solution.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = 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(DÂ» O.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

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

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!

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.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

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

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.

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