 1.6.1.6.1: If the composite functions then the function is the _______ functio...
 1.6.1.6.2: The domain of is the _______ of and the _______ of is the range of
 1.6.1.6.3: The graphs of and are reflections of each other in the line _______ .
 1.6.1.6.4: To have an inverse function, a function must be _______ ; that is, ...
 1.6.1.6.5: To have an inverse function, a function must be _______ ; that is, ...
 1.6.1.6.6: In Exercises 18, find the inverse function of informally. Verify th...
 1.6.1.6.7: In Exercises 18, find the inverse function of informally. Verify th...
 1.6.1.6.8: In Exercises 18, find the inverse function of informally. Verify th...
 1.6.1.6.9: In Exercises 914, (a) show that and are inverse functions algebraic...
 1.6.1.6.10: In Exercises 914, (a) show that and are inverse functions algebraic...
 1.6.1.6.11: In Exercises 914, (a) show that and are inverse functions algebraic...
 1.6.1.6.12: In Exercises 914, (a) show that and are inverse functions algebraic...
 1.6.1.6.13: In Exercises 914, (a) show that and are inverse functions algebraic...
 1.6.1.6.14: In Exercises 914, (a) show that and are inverse functions algebraic...
 1.6.1.6.15: In Exercises 1520, show that and are inverse functions algebraicall...
 1.6.1.6.16: In Exercises 1520, show that and are inverse functions algebraicall...
 1.6.1.6.17: In Exercises 1520, show that and are inverse functions algebraicall...
 1.6.1.6.18: In Exercises 1520, show that and are inverse functions algebraicall...
 1.6.1.6.19: In Exercises 1520, show that and are inverse functions algebraicall...
 1.6.1.6.20: In Exercises 1520, show that and are inverse functions algebraicall...
 1.6.1.6.21: In Exercises 2124, match the graph of the function with the graph o...
 1.6.1.6.22: In Exercises 2124, match the graph of the function with the graph o...
 1.6.1.6.23: In Exercises 2124, match the graph of the function with the graph o...
 1.6.1.6.24: In Exercises 2124, match the graph of the function with the graph o...
 1.6.1.6.25: In Exercises 2528, show that and are inverse functions (a) graphica...
 1.6.1.6.26: In Exercises 2528, show that and are inverse functions (a) graphica...
 1.6.1.6.27: In Exercises 2528, show that and are inverse functions (a) graphica...
 1.6.1.6.28: In Exercises 2528, show that and are inverse functions (a) graphica...
 1.6.1.6.29: In Exercises 2934, determine if the graph is that of a function. If...
 1.6.1.6.30: In Exercises 2934, determine if the graph is that of a function. If...
 1.6.1.6.31: In Exercises 2934, determine if the graph is that of a function. If...
 1.6.1.6.32: In Exercises 2934, determine if the graph is that of a function. If...
 1.6.1.6.33: In Exercises 2934, determine if the graph is that of a function. If...
 1.6.1.6.34: In Exercises 2934, determine if the graph is that of a function. If...
 1.6.1.6.35: In Exercises 3546, use a graphing utility to graph the function and...
 1.6.1.6.36: In Exercises 3546, use a graphing utility to graph the function and...
 1.6.1.6.37: In Exercises 3546, use a graphing utility to graph the function and...
 1.6.1.6.38: In Exercises 3546, use a graphing utility to graph the function and...
 1.6.1.6.39: In Exercises 3546, use a graphing utility to graph the function and...
 1.6.1.6.40: In Exercises 3546, use a graphing utility to graph the function and...
 1.6.1.6.41: In Exercises 3546, use a graphing utility to graph the function and...
 1.6.1.6.42: In Exercises 3546, use a graphing utility to graph the function and...
 1.6.1.6.43: In Exercises 3546, use a graphing utility to graph the function and...
 1.6.1.6.44: In Exercises 3546, use a graphing utility to graph the function and...
 1.6.1.6.45: In Exercises 3546, use a graphing utility to graph the function and...
 1.6.1.6.46: In Exercises 3546, use a graphing utility to graph the function and...
 1.6.1.6.47: In Exercises 4758, determine algebraically whether the function is ...
 1.6.1.6.48: In Exercises 4758, determine algebraically whether the function is ...
 1.6.1.6.49: In Exercises 4758, determine algebraically whether the function is ...
 1.6.1.6.50: In Exercises 4758, determine algebraically whether the function is ...
 1.6.1.6.51: In Exercises 4758, determine algebraically whether the function is ...
 1.6.1.6.52: In Exercises 4758, determine algebraically whether the function is ...
 1.6.1.6.53: In Exercises 4758, determine algebraically whether the function is ...
 1.6.1.6.54: In Exercises 4758, determine algebraically whether the function is ...
 1.6.1.6.55: In Exercises 4758, determine algebraically whether the function is ...
 1.6.1.6.56: In Exercises 4758, determine algebraically whether the function is ...
 1.6.1.6.57: In Exercises 4758, determine algebraically whether the function is ...
 1.6.1.6.58: In Exercises 4758, determine algebraically whether the function is ...
 1.6.1.6.59: In Exercises 5968, find the inverse function of algebraically. Use ...
 1.6.1.6.60: In Exercises 5968, find the inverse function of algebraically. Use ...
 1.6.1.6.61: In Exercises 5968, find the inverse function of algebraically. Use ...
 1.6.1.6.62: In Exercises 5968, find the inverse function of algebraically. Use ...
 1.6.1.6.63: In Exercises 5968, find the inverse function of algebraically. Use ...
 1.6.1.6.64: In Exercises 5968, find the inverse function of algebraically. Use ...
 1.6.1.6.65: In Exercises 5968, find the inverse function of algebraically. Use ...
 1.6.1.6.66: In Exercises 5968, find the inverse function of algebraically. Use ...
 1.6.1.6.67: In Exercises 5968, find the inverse function of algebraically. Use ...
 1.6.1.6.68: In Exercises 5968, find the inverse function of algebraically. Use ...
 1.6.1.6.69: Think About It In Exercises 6978, restrict the domain of the functi...
 1.6.1.6.70: Think About It In Exercises 6978, restrict the domain of the functi...
 1.6.1.6.71: Think About It In Exercises 6978, restrict the domain of the functi...
 1.6.1.6.72: Think About It In Exercises 6978, restrict the domain of the functi...
 1.6.1.6.73: Think About It In Exercises 6978, restrict the domain of the functi...
 1.6.1.6.74: Think About It In Exercises 6978, restrict the domain of the functi...
 1.6.1.6.75: Think About It In Exercises 6978, restrict the domain of the functi...
 1.6.1.6.76: Think About It In Exercises 6978, restrict the domain of the functi...
 1.6.1.6.77: Think About It In Exercises 6978, restrict the domain of the functi...
 1.6.1.6.78: Think About It In Exercises 6978, restrict the domain of the functi...
 1.6.1.6.79: In Exercises 79 and 80, use the graph of the function to complete t...
 1.6.1.6.80: In Exercises 79 and 80, use the graph of the function to complete t...
 1.6.1.6.81: In Exercises 81 88, use the graphs of and to evaluate the function.
 1.6.1.6.82: In Exercises 81 88, use the graphs of and to evaluate the function.
 1.6.1.6.83: In Exercises 81 88, use the graphs of and to evaluate the function.
 1.6.1.6.84: In Exercises 81 88, use the graphs of and to evaluate the function.
 1.6.1.6.85: In Exercises 81 88, use the graphs of and to evaluate the function.
 1.6.1.6.86: In Exercises 81 88, use the graphs of and to evaluate the function.
 1.6.1.6.87: In Exercises 81 88, use the graphs of and to evaluate the function.
 1.6.1.6.88: In Exercises 81 88, use the graphs of and to evaluate the function.
 1.6.1.6.89: Graphical Reasoning In Exercises 8992, (a) use a graphing utility t...
 1.6.1.6.90: Graphical Reasoning In Exercises 8992, (a) use a graphing utility t...
 1.6.1.6.91: Graphical Reasoning In Exercises 8992, (a) use a graphing utility t...
 1.6.1.6.92: Graphical Reasoning In Exercises 8992, (a) use a graphing utility t...
 1.6.1.6.93: In Exercises 9398, use the functions and to find the indicated valu...
 1.6.1.6.94: In Exercises 9398, use the functions and to find the indicated valu...
 1.6.1.6.95: In Exercises 9398, use the functions and to find the indicated valu...
 1.6.1.6.96: In Exercises 9398, use the functions and to find the indicated valu...
 1.6.1.6.97: In Exercises 9398, use the functions and to find the indicated valu...
 1.6.1.6.98: In Exercises 9398, use the functions and to find the indicated valu...
 1.6.1.6.99: In Exercises 99102, use the functions and to find the specified fun...
 1.6.1.6.100: In Exercises 99102, use the functions and to find the specified fun...
 1.6.1.6.101: In Exercises 99102, use the functions and to find the specified fun...
 1.6.1.6.102: In Exercises 99102, use the functions and to find the specified fun...
 1.6.1.6.103: Shoe Sizes The table shows mens shoe sizes in the United States and...
 1.6.1.6.104: Shoe Sizes The table shows womens shoe sizes in the United States a...
 1.6.1.6.105: Transportation The total values of new car sales (in billions of do...
 1.6.1.6.106: Hourly Wage Your wage is $8.00 per hour plus $0.75 for each unit pr...
 1.6.1.6.107: True or False? In Exercises 107 and 108, determine whether the stat...
 1.6.1.6.108: True or False? In Exercises 107 and 108, determine whether the stat...
 1.6.1.6.109: Proof Prove that if and are onetoone functions,
 1.6.1.6.110: Proof Prove that if is a onetoone odd function, is an odd function.
 1.6.1.6.111: In Exercises 111114, decide whether the two functions shown in the ...
 1.6.1.6.112: In Exercises 111114, decide whether the two functions shown in the ...
 1.6.1.6.113: In Exercises 111114, decide whether the two functions shown in the ...
 1.6.1.6.114: In Exercises 111114, decide whether the two functions shown in the ...
 1.6.1.6.115: In Exercises 115118, determine if the situation could be represente...
 1.6.1.6.116: In Exercises 115118, determine if the situation could be represente...
 1.6.1.6.117: In Exercises 115118, determine if the situation could be represente...
 1.6.1.6.118: In Exercises 115118, determine if the situation could be represente...
 1.6.1.6.119: In Exercises 119122, write the rational expression in simplest form.
 1.6.1.6.120: In Exercises 119122, write the rational expression in simplest form.
 1.6.1.6.121: In Exercises 119122, write the rational expression in simplest form.
 1.6.1.6.122: In Exercises 119122, write the rational expression in simplest form.
 1.6.1.6.123: In Exercises 123128, determine whether the equation represents as a...
 1.6.1.6.124: In Exercises 123128, determine whether the equation represents as a...
 1.6.1.6.125: In Exercises 123128, determine whether the equation represents as a...
 1.6.1.6.126: In Exercises 123128, determine whether the equation represents as a...
 1.6.1.6.127: In Exercises 123128, determine whether the equation represents as a...
 1.6.1.6.128: In Exercises 123128, determine whether the equation represents as a...
Solutions for Chapter 1.6: Inverse Functions
Full solutions for Precalculus With Limits A Graphing Approach  5th Edition
ISBN: 9780618851522
Solutions for Chapter 1.6: Inverse Functions
Get Full SolutionsPrecalculus With Limits A Graphing Approach was written by and is associated to the ISBN: 9780618851522. Since 128 problems in chapter 1.6: Inverse Functions have been answered, more than 44106 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 1.6: Inverse Functions includes 128 full stepbystep solutions. This textbook survival guide was created for the textbook: Precalculus With Limits A Graphing Approach, edition: 5.

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).

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Dimension of vector space
dim(V) = number of vectors in any basis for V.

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!).

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

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

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

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

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.

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.

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.

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

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

Solvable system Ax = b.
The right side b is in the column space of A.

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

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