 2.6.a: Use the graphs of and in Figure 2.65 to make a table showing the va...
 2.6.1: Two functions and can be combined by the arithmetic operations of _...
 2.6.b: Use the graphs of and in Figure 2.65 to make a table showing the va...
 2.6.2: The ________ of the function with is
 2.6.3: The domain of is all in the domain of such that _______ is in the d...
 2.6.4: To decompose a composite function, look for an ________ function 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: f x x 2, g x x 2
 2.6.10: f x 2x 5, g x 2 x f
 2.6.11: f x x g x 4x 5 2
 2.6.12: f x 3x 1, g x 5x 4
 2.6.13: f x x g x 1 x 2
 2.6.14: g x x2 x2 1 f
 2.6.15: g x 1 x2 f
 2.6.16: g x x3 f
 2.6.17: f g 2
 2.6.18: f g 1 f
 2.6.19: f g 0
 2.6.20: f g 1
 2.6.21: f g 3t
 2.6.22: f g t 2
 2.6.23: fg 6
 2.6.24: fg 6
 2.6.25: f g 5
 2.6.26: f g 0
 2.6.27: f g 1 g 3 f
 2.6.28: fg 5 f 4
 2.6.29: f x g x x 1 1
 2.6.30: f x g x x 4 1
 2.6.31: f x x g x 2x 2
 2.6.32: f x 4 x g x x 2
 2.6.33: g x x3 10 f x
 2.6.34: f x g x x
 2.6.35: f x 3x 2, g x x 5 f
 2.6.36: f x x 2 1 2
 2.6.37: f x x g x x 1 2,
 2.6.38: f x 3x 5, g x 5 x
 2.6.39: f x 3 1
 2.6.40: g x 1 x f
 2.6.41: g x x 2 f
 2.6.42: f x 3 1
 2.6.43: f x
 2.6.44: g x x6 f
 2.6.45: f x x , g x x 6
 2.6.46: f x g x 3 x
 2.6.47: f x g x x 3
 2.6.48: f x g x x 1 3
 2.6.49: (a)
 2.6.50: (a)
 2.6.51: (a)
 2.6.52: (a)
 2.6.53: h x 2x 12
 2.6.54: h x 1 x3 h
 2.6.55: h x h x 9 x 3 x 2 4 h x
 2.6.56: h x 9 x
 2.6.57: h x 1 x 2
 2.6.58: h x
 2.6.59: h x x2 3 4 x2 h
 2.6.60: h x 27x 3 6x 10 27x 3 h
 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: of a new hybrid car is dollars. The dealership advertises a factory...
 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 in...
 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 Algebra and Trigonometry  8th Edition
ISBN: 9781439048474
Solutions for Chapter 2.6: Combinations of Functions: Composite Functions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 86 problems in chapter 2.6: Combinations of Functions: Composite Functions have been answered, more than 47457 students have viewed full stepbystep solutions from this chapter. Algebra and Trigonometry was written by and is associated to the ISBN: 9781439048474. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 8. Chapter 2.6: Combinations of Functions: Composite Functions includes 86 full stepbystep solutions.

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

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

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

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

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

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.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.