 5.2.1: Is the set of ordered pairs {(1, 3), (2, 3), (1, 2)} a function? W...
 5.2.2: Where is the function f1x2 = x2 increasing? Where is it decreasing?...
 5.2.3: What is the domain of f1x2 = x + 5 x2 + 3x  18? (pp. 6465)
 5.2.4: Simplify: 1 x + 1 1 x2  1 (pp. A39A40)
 5.2.5: If x1 and x2 are two different inputs of a function f, then f is on...
 5.2.6: If every horizontal line intersects the graph of a function f at no...
 5.2.7: If f is a onetoone function and f(3) = 8, then f 1 (8) = .
 5.2.8: If f 1 denotes the inverse of a function f, then the graphs of f a...
 5.2.9: If the domain of a onetoone function f is 34, ), the range of its...
 5.2.10: If f and g are inverse functions, the domain of f is the same as th...
 5.2.11: In 1118, determine whether the function is onetoone.
 5.2.12: In 1118, determine whether the function is onetoone.
 5.2.13: In 1118, determine whether the function is onetoone.
 5.2.14: In 1118, determine whether the function is onetoone.
 5.2.15: In 1118, determine whether the function is onetoone.
 5.2.16: In 1118, determine whether the function is onetoone.
 5.2.17: In 1118, determine whether the function is onetoone.
 5.2.18: In 1118, determine whether the function is onetoone.
 5.2.19: In 1924, the graph of a function f is given. Use the horizontallin...
 5.2.20: In 1924, the graph of a function f is given. Use the horizontallin...
 5.2.21: In 1924, the graph of a function f is given. Use the horizontallin...
 5.2.22: In 1924, the graph of a function f is given. Use the horizontallin...
 5.2.23: In 1924, the graph of a function f is given. Use the horizontallin...
 5.2.24: In 1924, the graph of a function f is given. Use the horizontallin...
 5.2.25: In 2532, find the inverse of each onetoone function. State the do...
 5.2.26: In 2532, find the inverse of each onetoone function. State the do...
 5.2.27: In 2532, find the inverse of each onetoone function. State the do...
 5.2.28: In 2532, find the inverse of each onetoone function. State the do...
 5.2.29: In 2532, find the inverse of each onetoone function. State the do...
 5.2.30: In 2532, find the inverse of each onetoone function. State the do...
 5.2.31: In 2532, find the inverse of each onetoone function. State the do...
 5.2.32: In 2532, find the inverse of each onetoone function. State the do...
 5.2.33: In 33 42, verify that the functions f and g are inverses of each ot...
 5.2.34: In 33 42, verify that the functions f and g are inverses of each ot...
 5.2.35: In 33 42, verify that the functions f and g are inverses of each ot...
 5.2.36: In 33 42, verify that the functions f and g are inverses of each ot...
 5.2.37: In 33 42, verify that the functions f and g are inverses of each ot...
 5.2.38: In 33 42, verify that the functions f and g are inverses of each ot...
 5.2.39: In 33 42, verify that the functions f and g are inverses of each ot...
 5.2.40: In 33 42, verify that the functions f and g are inverses of each ot...
 5.2.41: In 33 42, verify that the functions f and g are inverses of each ot...
 5.2.42: In 33 42, verify that the functions f and g are inverses of each ot...
 5.2.43: In 43 48, the graph of a onetoone function f is given. Draw the g...
 5.2.44: In 43 48, the graph of a onetoone function f is given. Draw the g...
 5.2.45: In 43 48, the graph of a onetoone function f is given. Draw the g...
 5.2.46: In 43 48, the graph of a onetoone function f is given. Draw the g...
 5.2.47: In 43 48, the graph of a onetoone function f is given. Draw the g...
 5.2.48: In 43 48, the graph of a onetoone function f is given. Draw the g...
 5.2.49: In 49 60, the function f is onetoone. Find its inverse and check ...
 5.2.50: In 49 60, the function f is onetoone. Find its inverse and check ...
 5.2.51: In 49 60, the function f is onetoone. Find its inverse and check ...
 5.2.52: In 49 60, the function f is onetoone. Find its inverse and check ...
 5.2.53: In 49 60, the function f is onetoone. Find its inverse and check ...
 5.2.54: In 49 60, the function f is onetoone. Find its inverse and check ...
 5.2.55: In 49 60, the function f is onetoone. Find its inverse and check ...
 5.2.56: In 49 60, the function f is onetoone. Find its inverse and check ...
 5.2.57: In 49 60, the function f is onetoone. Find its inverse and check ...
 5.2.58: In 49 60, the function f is onetoone. Find its inverse and check ...
 5.2.59: In 49 60, the function f is onetoone. Find its inverse and check ...
 5.2.60: In 49 60, the function f is onetoone. Find its inverse and check ...
 5.2.61: In 6172, the function f is onetoone. Find its inverse and check y...
 5.2.62: In 6172, the function f is onetoone. Find its inverse and check y...
 5.2.63: In 6172, the function f is onetoone. Find its inverse and check y...
 5.2.64: In 6172, the function f is onetoone. Find its inverse and check y...
 5.2.65: In 6172, the function f is onetoone. Find its inverse and check y...
 5.2.66: In 6172, the function f is onetoone. Find its inverse and check y...
 5.2.67: In 6172, the function f is onetoone. Find its inverse and check y...
 5.2.68: In 6172, the function f is onetoone. Find its inverse and check y...
 5.2.69: In 6172, the function f is onetoone. Find its inverse and check y...
 5.2.70: In 6172, the function f is onetoone. Find its inverse and check y...
 5.2.71: In 6172, the function f is onetoone. Find its inverse and check y...
 5.2.72: In 6172, the function f is onetoone. Find its inverse and check y...
 5.2.73: Use the graph of y = f1x2 given in to evaluate the following:
 5.2.74: Use the graph of y = f1x2 given in to evaluate the following: (a) f...
 5.2.75: If f172 = 13 and f is onetoone, what is f 1 1132?
 5.2.76: If g1 52 = 3 and g is onetoone, what is g1 132?
 5.2.77: The domain of a onetoone function f is [5, 2, and its range is [...
 5.2.78: The domain of a onetoone function f is [0, 2, and its range is [5...
 5.2.79: The domain of a onetoone function g is 1  , 04, and its range is...
 5.2.80: The domain of a onetoone function g is [0, 15], and its range is ...
 5.2.81: A function y = f1x2 is increasing on the interval (0, 5). What conc...
 5.2.82: A function y = f1x2 is decreasing on the interval (0, 5). What conc...
 5.2.83: Find the inverse of the linear function f1x2 = mx + b m 0
 5.2.84: Find the inverse of the function f1x2 = 2r2  x2 0 x r
 5.2.85: A function f has an inverse function. If the graph of f lies in qua...
 5.2.86: A function f has an inverse function. If the graph of f lies in qua...
 5.2.87: The function f1x2 = x is not onetoone. Find a suitable restrictio...
 5.2.88: The function f1x2 = x4 is not onetoone. Find a suitable restricti...
 5.2.89: Taking into account reaction time, the distance d (in feet) that a ...
 5.2.90: The head circumference C of a child is related to the height H of t...
 5.2.91: One model for the ideal body weight W for men (in kilograms) as a f...
 5.2.92: The function F1C2 = 9 5 C + 32 converts a temperature from C degree...
 5.2.93: The function T1g2 = 4750 + 0.251g  34,5002 represents the 2011 fed...
 5.2.94: The function T1g2 = 1700 + 0.151g  17,0002 represents the 2011 fed...
 5.2.95: SECTION 5.3 Exponential Functions 271 (b) Find the inverse of H and...
 5.2.96: The period T (in seconds) of a simple pendulum as a function of its...
 5.2.97: Given f1x2 = ax + b cx + d find f 1 1x2. If c 0, under what condit...
 5.2.98: Can a onetoone function and its inverse be equal? What must be tr...
 5.2.99: Draw the graph of a onetoone function that contains the points (...
 5.2.100: Give an example of a function whose domain is the set of real numbe...
 5.2.101: Is every odd function onetoone? Explain.
 5.2.102: Suppose that C(g) represents the cost C, in dollars, of manufacturi...
 5.2.103: Explain why the horizontalline test can be used to identify oneto...
Solutions for Chapter 5.2: OnetoOne Functions; Inverse Functions
Full solutions for Precalculus Enhanced with Graphing Utilities  6th Edition
ISBN: 9780132854351
Solutions for Chapter 5.2: OnetoOne Functions; Inverse Functions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 103 problems in chapter 5.2: OnetoOne Functions; Inverse Functions have been answered, more than 56212 students have viewed full stepbystep solutions from this chapter. Chapter 5.2: OnetoOne Functions; Inverse Functions includes 103 full stepbystep solutions. This textbook survival guide was created for the textbook: Precalculus Enhanced with Graphing Utilities, edition: 6. Precalculus Enhanced with Graphing Utilities was written by and is associated to the ISBN: 9780132854351.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

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

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

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.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

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.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Outer product uv T
= column times row = rank one matrix.

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.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

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.

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

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.