 2.3.1: Given that f 1x2 = 3x + 1, g1x2 = x2  2x  6, and h1x2 = x3 , find...
 2.3.2: Given that f 1x2 = 3x + 1, g1x2 = x2  2x  6, and h1x2 = x3 , find...
 2.3.3: Given that f 1x2 = 3x + 1, g1x2 = x2  2x  6, and h1x2 = x3 , find...
 2.3.4: Given that f 1x2 = 3x + 1, g1x2 = x2  2x  6, and h1x2 = x3 , find...
 2.3.5: Given that f 1x2 = 3x + 1, g1x2 = x2  2x  6, and h1x2 = x3 , find...
 2.3.6: Given that f 1x2 = 3x + 1, g1x2 = x2  2x  6, and h1x2 = x3 , find...
 2.3.7: Given that f 1x2 = 3x + 1, g1x2 = x2  2x  6, and h1x2 = x3 , find...
 2.3.8: Given that f 1x2 = 3x + 1, g1x2 = x2  2x  6, and h1x2 = x3 , find...
 2.3.9: Given that f 1x2 = 3x + 1, g1x2 = x2  2x  6, and h1x2 = x3 , find...
 2.3.10: Given that f 1x2 = 3x + 1, g1x2 = x2  2x  6, and h1x2 = x3 , find...
 2.3.11: Given that f 1x2 = 3x + 1, g1x2 = x2  2x  6, and h1x2 = x3 , find...
 2.3.12: Given that f 1x2 = 3x + 1, g1x2 = x2  2x  6, and h1x2 = x3 , find...
 2.3.13: Given that f 1x2 = 3x + 1, g1x2 = x2  2x  6, and h1x2 = x3 , find...
 2.3.14: Given that f 1x2 = 3x + 1, g1x2 = x2  2x  6, and h1x2 = x3 , find...
 2.3.15: Given that f 1x2 = 3x + 1, g1x2 = x2  2x  6, and h1x2 = x3 , find...
 2.3.16: Given that f 1x2 = 3x + 1, g1x2 = x2  2x  6, and h1x2 = x3 , find...
 2.3.17: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = x + 3, g...
 2.3.18: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = 45 x, g1...
 2.3.19: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = x + 1, g...
 2.3.20: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = 3x  2, ...
 2.3.21: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = x2  3, ...
 2.3.22: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = 4x2  x ...
 2.3.23: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = 41  5x,...
 2.3.24: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = 6x , g1x...
 2.3.25: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = 3x  7, ...
 2.3.26: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = 23 x  4...
 2.3.27: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = 2x + 1, ...
 2.3.28: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = 2x, g1x2...
 2.3.29: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = 20, g1x2...
 2.3.30: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = x4, g1x2...
 2.3.31: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = 2x + 5, ...
 2.3.32: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = x5  2, ...
 2.3.33: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = x2 + 2, ...
 2.3.34: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = 1  x2, ...
 2.3.35: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = 1  xx ,...
 2.3.36: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = 1x  2, ...
 2.3.37: Find 1f g21x2 and 1g f 21x2 and the domain of each.f 1x2 = x3  5x2...
 2.3.38: Find 1f g21x2 and 1g f 21x2 and the domain of each. f 1x2 = x  1, ...
 2.3.39: Find f 1x2 and g1x2 such that h1x2 = 1f g21x2. Answers may vary.h1x...
 2.3.40: Find f 1x2 and g1x2 such that h1x2 = 1f g21x2. Answers may vary.h1x...
 2.3.41: Find f 1x2 and g1x2 such that h1x2 = 1f g21x2. Answers may vary.h1x...
 2.3.42: Find f 1x2 and g1x2 such that h1x2 = 1f g21x2. Answers may vary.h1x...
 2.3.43: Find f 1x2 and g1x2 such that h1x2 = 1f g21x2. Answers may vary.h1x...
 2.3.44: Find f 1x2 and g1x2 such that h1x2 = 1f g21x2. Answers may vary.h1x...
 2.3.45: Find f 1x2 and g1x2 such that h1x2 = 1f g21x2. Answers may vary.h1x...
 2.3.46: Find f 1x2 and g1x2 such that h1x2 = 1f g21x2. Answers may vary.h1x...
 2.3.47: Find f 1x2 and g1x2 such that h1x2 = 1f g21x2. Answers may vary.h1x...
 2.3.48: Find f 1x2 and g1x2 such that h1x2 = 1f g21x2. Answers may vary.h1x...
 2.3.49: Find f 1x2 and g1x2 such that h1x2 = 1f g21x2. Answers may vary.h1x...
 2.3.50: Find f 1x2 and g1x2 such that h1x2 = 1f g21x2. Answers may vary.h1x...
 2.3.51: Ripple Spread. A stone is thrown into a pond, creating a circular r...
 2.3.52: The surface area S of a right circular cylinder is given by the for...
 2.3.53: A manufacturer of tools, selling rechargeable drills to a chain of ...
 2.3.54: Blouse Sizes. A blouse that is size x in Japan is size s1x2 in the ...
 2.3.55: Consider the following linear equations. Without graphing them, ans...
 2.3.56: Consider the following linear equations. Without graphing them, ans...
 2.3.57: Consider the following linear equations. Without graphing them, ans...
 2.3.58: Consider the following linear equations. Without graphing them, ans...
 2.3.59: Consider the following linear equations. Without graphing them, ans...
 2.3.60: Consider the following linear equations. Without graphing them, ans...
 2.3.61: Consider the following linear equations. Without graphing them, ans...
 2.3.62: Consider the following linear equations. Without graphing them, ans...
 2.3.63: Let p1a2 represent the number of pounds of grass seed required to s...
 2.3.64: Write equations of two functions f and g such that f g = g f = x. (...
Solutions for Chapter 2.3: The Composition of Functions
Full solutions for College Algebra: Graphs and Models  5th Edition
ISBN: 9780321783950
Solutions for Chapter 2.3: The Composition of Functions
Get Full SolutionsChapter 2.3: The Composition of Functions includes 64 full stepbystep solutions. Since 64 problems in chapter 2.3: The Composition of Functions have been answered, more than 28924 students have viewed full stepbystep solutions from this chapter. College Algebra: Graphs and Models was written by and is associated to the ISBN: 9780321783950. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: College Algebra: Graphs and Models, edition: 5.

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

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.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

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.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

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

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

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

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 .

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).

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

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.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

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.

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

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

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