 7.2.1: Find the inverse of each relation.
 7.2.2: Find the inverse of each relation.
 7.2.3: Find the inverse of each function. Then graph the function and its ...
 7.2.4: Find the inverse of each function. Then graph the function and its ...
 7.2.5: Find the inverse of each function. Then graph the function and its ...
 7.2.6: Find the value of the acceleration due to gravity in feet per secon...
 7.2.7: An object is accelerating at 50 feet per second squared. How fast i...
 7.2.8: Determine whether each pair of functions are inverse functions.
 7.2.9: Determine whether each pair of functions are inverse functions.
 7.2.10: Find the inverse of each relation.
 7.2.11: Find the inverse of each relation.
 7.2.12: Find the inverse of each relation.
 7.2.13: Find the inverse of each relation.
 7.2.14: Find the inverse of each relation.
 7.2.15: Find the inverse of each relation.
 7.2.16: Find the inverse of each function. Then graph the function and its ...
 7.2.17: Find the inverse of each function. Then graph the function and its ...
 7.2.18: Find the inverse of each function. Then graph the function and its ...
 7.2.19: Find the inverse of each function. Then graph the function and its ...
 7.2.20: Find the inverse of each function. Then graph the function and its ...
 7.2.21: Find the inverse of each function. Then graph the function and its ...
 7.2.22: Find the inverse of each function. Then graph the function and its ...
 7.2.23: Find the inverse of each function. Then graph the function and its ...
 7.2.24: Find the inverse of each function. Then graph the function and its ...
 7.2.25: Find the inverse of each function. Then graph the function and its ...
 7.2.26: Find the inverse of each function. Then graph the function and its ...
 7.2.27: Find the inverse of each function. Then graph the function and its ...
 7.2.28: Find the inverse of the function
 7.2.29: Use the inverse to find the radius of the circle whose area is 36 s...
 7.2.30: Determine whether each pair of functions are inverse functions.
 7.2.31: Determine whether each pair of functions are inverse functions.
 7.2.32: Determine whether each pair of functions are inverse functions.
 7.2.33: Determine whether each pair of functions are inverse functions.
 7.2.34: Determine whether each pair of functions are inverse functions.
 7.2.35: Determine whether each pair of functions are inverse functions.
 7.2.36: Write an equation that models this problem.
 7.2.37: Find the inverse.
 7.2.38: Emilias final number was 9. What was her original number?
 7.2.39: Find the inverse F 1 (x). Show that F(x) and F 1 (x) are inverses.
 7.2.40: Explain what purpose F 1 (x) serves
 7.2.41: Determine the values of n for which f(x) = x n has an inverse that ...
 7.2.42: Sketch a graph of a function f that satisfies the following conditi...
 7.2.43: Give an example of a function that is its own inverse
 7.2.44: Refer to the information on page 391 to explain how inverse functio...
 7.2.45: Which of the following is the inverse of the function f(x) = _3x  ...
 7.2.46: Which expression represents f(g(x)) if f(x) = x2 + 3 and g(x) = x ...
 7.2.47: If f(x) = 2x + 4, g(x) = x  1, and h(x) = x2, find each value
 7.2.48: If f(x) = 2x + 4, g(x) = x  1, and h(x) = x2, find each value
 7.2.49: If f(x) = 2x + 4, g(x) = x  1, and h(x) = x2, find each value
 7.2.50: List all of the possible rational zeros of each function
 7.2.51: List all of the possible rational zeros of each function
 7.2.52: Perform the indicated operations
 7.2.53: Perform the indicated operations
 7.2.54: Find the maximum and minimum values of the function f(x, y) = 2x + ...
 7.2.55: State whether the system of equations shown at the right is consist...
 7.2.56: The amount that a mailorder company charges for shipping and handl...
 7.2.57: Solve each equation or inequality. Check your solutions
 7.2.58: Solve each equation or inequality. Check your solutions
 7.2.59: Solve each equation or inequality. Check your solutions
 7.2.60: Solve each equation or inequality. Check your solutions
 7.2.61: Solve each equation or inequality. Check your solutions
 7.2.62: Solve each equation or inequality. Check your solutions
 7.2.63: Graph each inequality.
 7.2.64: Graph each inequality.
 7.2.65: Graph each inequality.
Solutions for Chapter 7.2: Inverse Functions and Relations
Full solutions for California Algebra 2: Concepts, Skills, and Problem Solving  1st Edition
ISBN: 9780078778568
Solutions for Chapter 7.2: Inverse Functions and Relations
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 65 problems in chapter 7.2: Inverse Functions and Relations have been answered, more than 42096 students have viewed full stepbystep solutions from this chapter. California Algebra 2: Concepts, Skills, and Problem Solving was written by and is associated to the ISBN: 9780078778568. This textbook survival guide was created for the textbook: California Algebra 2: Concepts, Skills, and Problem Solving, edition: 1. Chapter 7.2: Inverse Functions and Relations includes 65 full stepbystep solutions.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

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.

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].

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

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.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

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

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

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 •

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

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

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

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

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

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

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