 2.2.1: Given that f 1x2 = x2  3 and g1x2 = 2x + 1, find each of the follo...
 2.2.2: Given that f 1x2 = x2  3 and g1x2 = 2x + 1, find each of the follo...
 2.2.3: Given that f 1x2 = x2  3 and g1x2 = 2x + 1, find each of the follo...
 2.2.4: Given that f 1x2 = x2  3 and g1x2 = 2x + 1, find each of the follo...
 2.2.5: Given that f 1x2 = x2  3 and g1x2 = 2x + 1, find each of the follo...
 2.2.6: Given that f 1x2 = x2  3 and g1x2 = 2x + 1, find each of the follo...
 2.2.7: Given that f 1x2 = x2  3 and g1x2 = 2x + 1, find each of the follo...
 2.2.8: Given that f 1x2 = x2  3 and g1x2 = 2x + 1, find each of the follo...
 2.2.9: Given that f 1x2 = x2  3 and g1x2 = 2x + 1, find each of the follo...
 2.2.10: Given that f 1x2 = x2  3 and g1x2 = 2x + 1, find each of the follo...
 2.2.11: Given that h1x2 = x + 4 and g1x2 = 2x  1, find each of the followi...
 2.2.12: Given that h1x2 = x + 4 and g1x2 = 2x  1, find each of the followi...
 2.2.13: Given that h1x2 = x + 4 and g1x2 = 2x  1, find each of the followi...
 2.2.14: Given that h1x2 = x + 4 and g1x2 = 2x  1, find each of the followi...
 2.2.15: Given that h1x2 = x + 4 and g1x2 = 2x  1, find each of the followi...
 2.2.16: Given that h1x2 = x + 4 and g1x2 = 2x  1, find each of the followi...
 2.2.17: For each pair of functions in Exercises 1734: a) Find the domain of...
 2.2.18: For each pair of functions in Exercises 1734: a) Find the domain of...
 2.2.19: For each pair of functions in Exercises 1734: a) Find the domain of...
 2.2.20: For each pair of functions in Exercises 1734: a) Find the domain of...
 2.2.21: For each pair of functions in Exercises 1734: a) Find the domain of...
 2.2.22: For each pair of functions in Exercises 1734: a) Find the domain of...
 2.2.23: For each pair of functions in Exercises 1734: a) Find the domain of...
 2.2.24: For each pair of functions in Exercises 1734: a) Find the domain of...
 2.2.25: For each pair of functions in Exercises 1734: a) Find the domain of...
 2.2.26: For each pair of functions in Exercises 1734: a) Find the domain of...
 2.2.27: For each pair of functions in Exercises 1734: a) Find the domain of...
 2.2.28: For each pair of functions in Exercises 1734: a) Find the domain of...
 2.2.29: For each pair of functions in Exercises 1734: a) Find the domain of...
 2.2.30: For each pair of functions in Exercises 1734: a) Find the domain of...
 2.2.31: For each pair of functions in Exercises 1734: a) Find the domain of...
 2.2.32: For each pair of functions in Exercises 1734: a) Find the domain of...
 2.2.33: For each pair of functions in Exercises 1734: a) Find the domain of...
 2.2.34: For each pair of functions in Exercises 1734: a) Find the domain of...
 2.2.35: In Exercises 3540, consider the functions F and G as shown in the g...
 2.2.36: In Exercises 3540, consider the functions F and G as shown in the g...
 2.2.37: In Exercises 3540, consider the functions F and G as shown in the g...
 2.2.38: In Exercises 3540, consider the functions F and G as shown in the g...
 2.2.39: In Exercises 3540, consider the functions F and G as shown in the g...
 2.2.40: In Exercises 3540, consider the functions F and G as shown in the g...
 2.2.41: In Exercises 4146, consider the functions F and G as shown in the g...
 2.2.42: In Exercises 4146, consider the functions F and G as shown in the g...
 2.2.43: In Exercises 4146, consider the functions F and G as shown in the g...
 2.2.44: In Exercises 4146, consider the functions F and G as shown in the g...
 2.2.45: In Exercises 4146, consider the functions F and G as shown in the g...
 2.2.46: In Exercises 4146, consider the functions F and G as shown in the g...
 2.2.47: Total Cost, Revenue, and Profit. In economics, functions that invol...
 2.2.48: Total Cost, Revenue, and Profit. Given that R1x2 = 200x  x2 and C1...
 2.2.49: For each function f , construct and simplify the difference quotien...
 2.2.50: For each function f , construct and simplify the difference quotien...
 2.2.51: For each function f , construct and simplify the difference quotien...
 2.2.52: For each function f , construct and simplify the difference quotien...
 2.2.53: For each function f , construct and simplify the difference quotien...
 2.2.54: For each function f , construct and simplify the difference quotien...
 2.2.55: For each function f , construct and simplify the difference quotien...
 2.2.56: For each function f , construct and simplify the difference quotien...
 2.2.57: For each function f , construct and simplify the difference quotien...
 2.2.58: For each function f , construct and simplify the difference quotien...
 2.2.59: For each function f , construct and simplify the difference quotien...
 2.2.60: For each function f , construct and simplify the difference quotien...
 2.2.61: For each function f , construct and simplify the difference quotien...
 2.2.62: For each function f , construct and simplify the difference quotien...
 2.2.63: For each function f , construct and simplify the difference quotien...
 2.2.64: For each function f , construct and simplify the difference quotien...
 2.2.65: For each function f , construct and simplify the difference quotien...
 2.2.66: For each function f , construct and simplify the difference quotien...
 2.2.67: For each function f , construct and simplify the difference quotien...
 2.2.68: For each function f , construct and simplify the difference quotien...
 2.2.69: For each function f , construct and simplify the difference quotien...
 2.2.70: For each function f , construct and simplify the difference quotien...
 2.2.71: Graph the equation.y = 3x  1
 2.2.72: Graph the equation.2x + y = 4
 2.2.73: Graph the equation.x  3y = 3
 2.2.74: Graph the equation.y = x2 + 1
 2.2.75: Write equations for two functions f and g such that the domain of f...
 2.2.76: For functions h and f , find the domain of h + f , h  f , hf , and...
 2.2.77: Find the domain of 1h>g21x2 given that h1x2 = 5x 3x  7 and g1x2 = ...
Solutions for Chapter 2.2: The Algebra of Functions
Full solutions for College Algebra: Graphs and Models  5th Edition
ISBN: 9780321783950
Solutions for Chapter 2.2: The Algebra of Functions
Get Full SolutionsThis textbook survival guide was created for the textbook: College Algebra: Graphs and Models, edition: 5. Chapter 2.2: The Algebra of Functions includes 77 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 77 problems in chapter 2.2: The Algebra of Functions have been answered, more than 27672 students have viewed full stepbystep solutions from this chapter. College Algebra: Graphs and Models was written by and is associated to the ISBN: 9780321783950.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

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

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

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.

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

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

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 .

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

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

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

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

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.

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!

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

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

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.