 2.6.1: Fill in the blanks. Two functions and can be combined by the arithm...
 2.6.2: Fill in the blanks. The ________ of the function with is
 2.6.3: Fill in the blanks. The domain of is all in the domain of such that...
 2.6.4: Fill in the blanks. To decompose a composite function, look for an ...
 2.6.5: In Exercises 5 8, use the graphs of and to graph To print an enlarg...
 2.6.6: In Exercises 5 8, use the graphs of and to graph To print an enlarg...
 2.6.7: In Exercises 5 8, use the graphs of and to graph To print an enlarg...
 2.6.8: In Exercises 5 8, use the graphs of and to graph To print an enlarg...
 2.6.9: In Exercises 916, find (a) (b) (c) and (d) What is the domain of
 2.6.10: In Exercises 916, find (a) (b) (c) and (d) What is the domain of
 2.6.11: In Exercises 916, find (a) (b) (c) and (d) What is the domain of
 2.6.12: In Exercises 916, find (a) (b) (c) and (d) What is the domain of
 2.6.13: In Exercises 916, find (a) (b) (c) and (d) What is the domain of
 2.6.14: In Exercises 916, find (a) (b) (c) and (d) What is the domain of
 2.6.15: In Exercises 916, find (a) (b) (c) and (d) What is the domain of
 2.6.16: In Exercises 916, find (a) (b) (c) and (d) What is the domain of
 2.6.17: In Exercises 1728, evaluate the indicated function for and
 2.6.18: In Exercises 1728, evaluate the indicated function for and
 2.6.19: In Exercises 1728, evaluate the indicated function for and
 2.6.20: In Exercises 1728, evaluate the indicated function for and
 2.6.21: In Exercises 1728, evaluate the indicated function for and
 2.6.22: In Exercises 1728, evaluate the indicated function for and
 2.6.23: In Exercises 1728, evaluate the indicated function for and
 2.6.24: In Exercises 1728, evaluate the indicated function for and
 2.6.25: In Exercises 1728, evaluate the indicated function for and
 2.6.26: In Exercises 1728, evaluate the indicated function for and
 2.6.27: In Exercises 1728, evaluate the indicated function for and
 2.6.28: In Exercises 1728, evaluate the indicated function for and
 2.6.29: In Exercises 2932, graph the functions and on the same set of coord...
 2.6.30: In Exercises 2932, graph the functions and on the same set of coord...
 2.6.31: In Exercises 2932, graph the functions and on the same set of coord...
 2.6.32: In Exercises 2932, graph the functions and on the same set of coord...
 2.6.33: GRAPHICAL REASONING In Exercises 3336, use a graphing utility to gr...
 2.6.34: GRAPHICAL REASONING In Exercises 3336, use a graphing utility to gr...
 2.6.35: GRAPHICAL REASONING In Exercises 3336, use a graphing utility to gr...
 2.6.36: GRAPHICAL REASONING In Exercises 3336, use a graphing utility to gr...
 2.6.37: In Exercises 37 40, find (a) (b) and
 2.6.38: In Exercises 37 40, find (a) (b) and
 2.6.39: In Exercises 37 40, find (a) (b) and
 2.6.40: In Exercises 37 40, find (a) (b) and
 2.6.41: In Exercises 4148, find (a) and (b) Find the domain of each functio...
 2.6.42: In Exercises 4148, find (a) and (b) Find the domain of each functio...
 2.6.43: In Exercises 4148, find (a) and (b) Find the domain of each functio...
 2.6.44: In Exercises 4148, find (a) and (b) Find the domain of each functio...
 2.6.45: In Exercises 4148, find (a) and (b) Find the domain of each functio...
 2.6.46: In Exercises 4148, find (a) and (b) Find the domain of each functio...
 2.6.47: In Exercises 4148, find (a) and (b) Find the domain of each functio...
 2.6.48: In Exercises 4148, find (a) and (b) Find the domain of each functio...
 2.6.49: In Exercises 4952, use the graphs of and to evaluate the functions.
 2.6.50: In Exercises 4952, use the graphs of and to evaluate the functions.
 2.6.51: In Exercises 4952, use the graphs of and to evaluate the functions.
 2.6.52: In Exercises 4952, use the graphs of and to evaluate the functions.
 2.6.53: In Exercises 53 60, find two functions and such that (There are man...
 2.6.54: In Exercises 53 60, find two functions and such that (There are man...
 2.6.55: In Exercises 53 60, find two functions and such that (There are man...
 2.6.56: In Exercises 53 60, find two functions and such that (There are man...
 2.6.57: In Exercises 53 60, find two functions and such that (There are man...
 2.6.58: In Exercises 53 60, find two functions and such that (There are man...
 2.6.59: In Exercises 53 60, find two functions and such that (There are man...
 2.6.60: In Exercises 53 60, find two functions and such that (There are man...
 2.6.61: STOPPING DISTANCE The research and development department of an aut...
 2.6.62: SALES From 2003 through 2008, the sales (in thousands of dollars) f...
 2.6.63: VITAL STATISTICS Let be the number of births in the United States i...
 2.6.64: PETS Let be the number of dogs in the United States in year and let...
 2.6.65: MILITARY PERSONNEL The total numbers of Navy personnel (in thousand...
 2.6.66: SPORTS The numbers of people playing tennis (in millions) in the Un...
 2.6.67: Find and interpret
 2.6.68: Evaluate and for the years 2010 and 2012. What does each function v...
 2.6.69: GRAPHICAL REASONING An electronically controlled thermostat in a ho...
 2.6.70: GEOMETRY A square concrete foundation is prepared as a base for a c...
 2.6.71: RIPPLES A pebble is dropped into a calm pond, causing ripples in th...
 2.6.72: POLLUTION The spread of a contaminant is increasing in a circular p...
 2.6.73: BACTERIA COUNT The number of bacteria in a refrigerated food is giv...
 2.6.74: COST The weekly cost of producing units in a manufacturing process ...
 2.6.75: SALARY You are a sales representative for a clothing manufacturer. ...
 2.6.76: CONSUMER AWARENESS The suggested retail price of a new hybrid car i...
 2.6.77: If and then
 2.6.78: If you are given two functions and , you can calculate if and only ...
 2.6.79: (a) Write a composite function that gives the oldest siblings age i...
 2.6.80: (a) Write a composite function that gives the youngest siblings age...
 2.6.81: PROOF Prove that the product of two odd functions is an even functi...
 2.6.82: CONJECTURE Use examples to hypothesize whether the product of an od...
 2.6.83: PROOF (a) Given a function prove that is even and is odd, where and...
 2.6.84: CAPSTONE Consider the functions and (a) Find and its domain. (b) Fi...
Solutions for Chapter 2.6: COMBINATIONS OF FUNCTIONS: COMPOSITE FUNCTIONS
Full solutions for College Algebra  8th Edition
ISBN: 9781439048696
Solutions for Chapter 2.6: COMBINATIONS OF FUNCTIONS: COMPOSITE FUNCTIONS
Get Full SolutionsSince 84 problems in chapter 2.6: COMBINATIONS OF FUNCTIONS: COMPOSITE FUNCTIONS have been answered, more than 31099 students have viewed full stepbystep solutions from this chapter. College Algebra was written by and is associated to the ISBN: 9781439048696. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2.6: COMBINATIONS OF FUNCTIONS: COMPOSITE FUNCTIONS includes 84 full stepbystep solutions. This textbook survival guide was created for the textbook: College Algebra , edition: 8.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

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.

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].

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 .

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

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.

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.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = 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 •

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

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

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!

Solvable system Ax = b.
The right side b is in the column space of A.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).