 3.4.1: How does one find the domain of the quotient of two functions, f _ g ?
 3.4.2: What is the composition of two functions, f g ?
 3.4.3: If the order is reversed when composing two functions, can the resu...
 3.4.4: How do you find the domain for the composition of two functions, f g ?
 3.4.5: For the following exercises, determine the domain for each function...
 3.4.6: For the following exercises, determine the domain for each function...
 3.4.7: For the following exercises, determine the domain for each function...
 3.4.8: For the following exercises, determine the domain for each function...
 3.4.9: For the following exercises, determine the domain for each function...
 3.4.10: For the following exercises, determine the domain for each function...
 3.4.11: For the following exercise, find the indicated function given f(x) ...
 3.4.12: For the following exercises, use each pair of functions to find f(g...
 3.4.13: For the following exercises, use each pair of functions to find f(g...
 3.4.14: For the following exercises, use each pair of functions to find f(g...
 3.4.15: For the following exercises, use each pair of functions to find f(g...
 3.4.16: For the following exercises, use each pair of functions to find f(g...
 3.4.17: For the following exercises, use each pair of functions to find f(g...
 3.4.18: For the following exercises, use each set of functions to find f(g(...
 3.4.19: For the following exercises, use each set of functions to find f(g(...
 3.4.20: Given f(x) = _ 1 x , and g(x) = x 3, find the following: a. (f g)(x...
 3.4.21: Given f(x) = 2 4x and g(x) = _ 3 x , find the following: a. ( g f )...
 3.4.22: Given the functions f(x) = _ 1 x x and g(x) = _ 1 1 + x2 , find the...
 3.4.23: Given functions p(x) = _ 1 x and m(x) = x 2 4, state the domain of ...
 3.4.24: Given functions q(x) = _ 1 x and h(x) = x2 9, state the domain of e...
 3.4.25: For f(x) = _ 1 x and g(x) = x 1 , write the domain of (f g)(x) in i...
 3.4.26: For the following exercises, find functions f(x) and g(x) so the gi...
 3.4.27: For the following exercises, find functions f(x) and g(x) so the gi...
 3.4.28: For the following exercises, find functions f(x) and g(x) so the gi...
 3.4.29: For the following exercises, find functions f(x) and g(x) so the gi...
 3.4.30: For the following exercises, find functions f(x) and g(x) so the gi...
 3.4.31: For the following exercises, find functions f(x) and g(x) so the gi...
 3.4.32: For the following exercises, find functions f(x) and g(x) so the gi...
 3.4.33: For the following exercises, find functions f(x) and g(x) so the gi...
 3.4.34: For the following exercises, find functions f(x) and g(x) so the gi...
 3.4.35: For the following exercises, find functions f(x) and g(x) so the gi...
 3.4.36: For the following exercises, find functions f(x) and g(x) so the gi...
 3.4.37: For the following exercises, find functions f(x) and g(x) so the gi...
 3.4.38: For the following exercises, find functions f(x) and g(x) so the gi...
 3.4.39: For the following exercises, find functions f(x) and g(x) so the gi...
 3.4.40: For the following exercises, find functions f(x) and g(x) so the gi...
 3.4.41: For the following exercises, find functions f(x) and g(x) so the gi...
 3.4.42: For the following exercises, use the graphs of f, shown in Figure 4...
 3.4.43: For the following exercises, use the graphs of f, shown in Figure 4...
 3.4.44: For the following exercises, use the graphs of f, shown in Figure 4...
 3.4.45: For the following exercises, use the graphs of f, shown in Figure 4...
 3.4.46: For the following exercises, use the graphs of f, shown in Figure 4...
 3.4.47: For the following exercises, use the graphs of f, shown in Figure 4...
 3.4.48: For the following exercises, use the graphs of f, shown in Figure 4...
 3.4.49: For the following exercises, use the graphs of f, shown in Figure 4...
 3.4.50: For the following exercises, use graphs of f(x), shown in Figure 6,...
 3.4.51: For the following exercises, use graphs of f(x), shown in Figure 6,...
 3.4.52: For the following exercises, use graphs of f(x), shown in Figure 6,...
 3.4.53: For the following exercises, use graphs of f(x), shown in Figure 6,...
 3.4.54: For the following exercises, use graphs of f(x), shown in Figure 6,...
 3.4.55: For the following exercises, use graphs of f(x), shown in Figure 6,...
 3.4.56: For the following exercises, use graphs of f(x), shown in Figure 6,...
 3.4.57: For the following exercises, use graphs of f(x), shown in Figure 6,...
 3.4.58: For the following exercises, use the function values for f and g sh...
 3.4.59: For the following exercises, use the function values for f and g sh...
 3.4.60: For the following exercises, use the function values for f and g sh...
 3.4.61: For the following exercises, use the function values for f and g sh...
 3.4.62: For the following exercises, use the function values for f and g sh...
 3.4.63: For the following exercises, use the function values for f and g sh...
 3.4.64: For the following exercises, use the function values for f and g sh...
 3.4.65: For the following exercises, use the function values for f and g sh...
 3.4.66: For the following exercises, use the function values for f and g sh...
 3.4.67: For the following exercises, use the function values for f and g sh...
 3.4.68: For the following exercises, use the function values for f and g sh...
 3.4.69: For the following exercises, use the function values for f and g sh...
 3.4.70: For the following exercises, use the function values for f and g sh...
 3.4.71: For the following exercises, use the function values for f and g sh...
 3.4.72: For the following exercises, use each pair of functions to find f(g...
 3.4.73: For the following exercises, use each pair of functions to find f(g...
 3.4.74: For the following exercises, use each pair of functions to find f(g...
 3.4.75: For the following exercises, use each pair of functions to find f(g...
 3.4.76: For the following exercises, use the functions f(x) = 2x2 + 1 and g...
 3.4.77: For the following exercises, use the functions f(x) = 2x2 + 1 and g...
 3.4.78: For the following exercises, use the functions f(x) = 2x2 + 1 and g...
 3.4.79: For the following exercises, use the functions f(x) = 2x2 + 1 and g...
 3.4.80: For the following exercises, use f(x) = x3 + 1 and g(x) = 3 x 1 . F...
 3.4.81: For the following exercises, use f(x) = x3 + 1 and g(x) = 3 x 1 . F...
 3.4.82: For the following exercises, use f(x) = x3 + 1 and g(x) = 3 x 1 . W...
 3.4.83: For the following exercises, use f(x) = x3 + 1 and g(x) = 3 x 1 . W...
 3.4.84: For the following exercises, use f(x) = x3 + 1 and g(x) = 3 x 1 . L...
 3.4.85: For the following exercises, let F(x) = (x + 1)5 , f(x) = x5 , and ...
 3.4.86: For the following exercises, let F(x) = (x + 1)5 , f(x) = x5 , and ...
 3.4.87: For the following exercises, find the composition when f(x) = x2 + ...
 3.4.88: For the following exercises, find the composition when f(x) = x2 + ...
 3.4.89: For the following exercises, find the composition when f(x) = x2 + ...
 3.4.90: The function D(p) gives the number of items that will be demanded w...
 3.4.91: The function A(d) gives the pain level on a scale of 0 to 10 experi...
 3.4.92: A store offers customers a 30% discount on the price x of selected ...
 3.4.93: A rain drop hitting a lake makes a circular ripple. If the radius, ...
 3.4.94: A forest fire leaves behind an area of grass burned in an expanding...
 3.4.95: Use the function you found in the previous exercise to find the tot...
 3.4.96: The radius r, in inches, of a spherical balloon is related to the v...
 3.4.97: The number of bacteria in a refrigerated food product is given by N...
Solutions for Chapter 3.4: COMPOSITION OF FUNCTIONS
Full solutions for College Algebra  1st Edition
ISBN: 9781938168383
Solutions for Chapter 3.4: COMPOSITION OF FUNCTIONS
Get Full SolutionsChapter 3.4: COMPOSITION OF FUNCTIONS includes 97 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 97 problems in chapter 3.4: COMPOSITION OF FUNCTIONS have been answered, more than 8671 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: College Algebra, edition: 1. College Algebra was written by Patricia and is associated to the ISBN: 9781938168383.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

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

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to 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.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

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

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = 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 .

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

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.

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

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).

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

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.

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.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).
I don't want to reset my password
Need help? Contact support
Having trouble accessing your account? Let us help you, contact support at +1(510) 9441054 or support@studysoup.com
Forgot password? Reset it here