 6.1.1: Find1x2 = 4x2 f132 + 5x
 6.1.2: Find if f1x2 = 4  2x
 6.1.3: Find the domain of the function f1x2 = x2  1 x2  25 .
 6.1.4: Given two functions f and g, the , denoted , is defined by
 6.1.5: True or False f1g1x22 = f1x2 # g(x).
 6.1.6: True or False The domain of the composite function 1f ! g21x2 is th...
 6.1.7: In 7 and 8, evaluate each expression using the values given in the ...
 6.1.8: In 7 and 8, evaluate each expression using the values given in the ...
 6.1.9: In 9 and 10, evaluate each expression using the graphs of and shown...
 6.1.10: In 9 and 10, evaluate each expression using the graphs of and shown...
 6.1.11: In 1120, for the given functions and , find: (a) 1f ! g2142 (b) 1g ...
 6.1.12: In 1120, for the given functions and , find: (a) 1f ! g2142 (b) 1g ...
 6.1.13: In 1120, for the given functions and , find: (a) 1f ! g2142 (b) 1g ...
 6.1.14: In 1120, for the given functions and , find: (a) 1f ! g2142 (b) 1g ...
 6.1.15: In 1120, for the given functions and , find: (a) 1f ! g2142 (b) 1g ...
 6.1.16: In 1120, for the given functions and , find: (a) 1f ! g2142 (b) 1g ...
 6.1.17: In 1120, for the given functions and , find: (a) 1f ! g2142 (b) 1g ...
 6.1.18: In 1120, for the given functions and , find: (a) 1f ! g2142 (b) 1g ...
 6.1.19: In 1120, for the given functions and , find: (a) 1f ! g2142 (b) 1g ...
 6.1.20: In 1120, for the given functions and , find: (a) 1f ! g2142 (b) 1g ...
 6.1.21: In 2128, find the domain of the composite function f ! g.f1x2 = 3 x...
 6.1.22: In 2128, find the domain of the composite function f ! g.f1x2 = 1 x...
 6.1.23: In 2128, find the domain of the composite function f ! g. f1x2 = xx...
 6.1.24: In 2128, find the domain of the composite function f ! g. f1x2 = xx...
 6.1.25: In 2128, find the domain of the composite function f ! g. f1x2 = 1x...
 6.1.26: In 2128, find the domain of the composite function f ! g. f1x2 = x ...
 6.1.27: In 2128, find the domain of the composite function f ! g. f1x2 = x2...
 6.1.28: In 2128, find the domain of the composite function f ! g. f1x2 = x2...
 6.1.29: In 2944, for the given functions and find: (a) (b) (c) (d) State th...
 6.1.30: In 2944, for the given functions and find: (a) (b) (c) (d) State th...
 6.1.31: In 2944, for the given functions and find: (a) (b) (c) (d) State th...
 6.1.32: In 2944, for the given functions and find: (a) (b) (c) (d) State th...
 6.1.33: In 2944, for the given functions and find: (a) (b) (c) (d) State th...
 6.1.34: In 2944, for the given functions and find: (a) (b) (c) (d) State th...
 6.1.35: In 2944, for the given functions and find: (a) (b) (c) (d) State th...
 6.1.36: In 2944, for the given functions and find: (a) (b) (c) (d) State th...
 6.1.37: In 2944, for the given functions and find: (a) (b) (c) (d) State th...
 6.1.38: In 2944, for the given functions and find: (a) (b) (c) (d) State th...
 6.1.39: In 2944, for the given functions and find: (a) (b) (c) (d) State th...
 6.1.40: In 2944, for the given functions and find: (a) (b) (c) (d) State th...
 6.1.41: In 2944, for the given functions and find: (a) (b) (c) (d) State th...
 6.1.42: In 2944, for the given functions and find: (a) (b) (c) (d) State th...
 6.1.43: In 2944, for the given functions and find: (a) (b) (c) (d) State th...
 6.1.44: In 2944, for the given functions and find: (a) (b) (c) (d) State th...
 6.1.45: In 4552,show that 1f ! g21x2 = 1g ! f21x2 = x. f1x2 = 2x; g1x2 = 12x
 6.1.46: In 4552,show that 1f ! g21x2 = 1g ! f21x2 = x. f1x2 = 4x; g1x2 = 14x
 6.1.47: In 4552,show that 1f ! g21x2 = 1g ! f21x2 = x. f1x2 = x3; g1x2 = 13 x
 6.1.48: In 4552,show that 1f ! g21x2 = 1g ! f21x2 = x. f1x2 = x + 5; g1x2 =...
 6.1.49: In 4552,show that 1f ! g21x2 = 1g ! f21x2 = x. f1x2 = 2x  6; g1x2 ...
 6.1.50: In 4552,show that 1f ! g21x2 = 1g ! f21x2 = x. f1x2 = 4  3x; g1x2 ...
 6.1.51: In 4552,show that 1f ! g21x2 = 1g ! f21x2 = x. f1x2 = ax + b; g1x2 ...
 6.1.52: In 4552,show that 1f ! g21x2 = 1g ! f21x2 = x. f1x2 = 1x ; g1x2 = 1x
 6.1.53: In 5358, find functions f and g so that f ! g = H. H1x2 = 12x + 324
 6.1.54: In 5358, find functions f and g so that f ! g = H. H1x2 = 11 + x223
 6.1.55: In 5358, find functions f and g so that f ! g = H. H1x2 = 4x2 + 1
 6.1.56: In 5358, find functions f and g so that f ! g = H. H1x2 = 41  x2
 6.1.57: In 5358, find functions f and g so that f ! g = H. H1x2 = 2x + 1
 6.1.58: In 5358, find functions f and g so that f ! g = H. H1x2 = 2x2 + 3
 6.1.59: If f1x2 = 2x 3  3x2 + 4x  1 and g1x2 = 2, find 1f ! g21x2 and 1g ...
 6.1.60: If f1x2 = x + 1x  1 find 1f ! f21x2.
 6.1.61: If f1x2 = 2x2 + 5 and g1x2 = 3x + a find a so that the graph of cro...
 6.1.62: If f1x2 = 3x2  7 and g1x2 = 2x + a find a so that the graph of cro...
 6.1.63: In 63 and 64, use the functions f and g to find: (a) (b) (c) the do...
 6.1.64: In 63 and 64, use the functions f and g to find: (a) (b) (c) the do...
 6.1.65: Surface Area of a Balloon The surface area S (in square meters) of ...
 6.1.66: Volume of a Balloon The volume V (in cubic meters) of the hotair b...
 6.1.67: Automobile Production The number N of cars produced at a certain fa...
 6.1.68: Environmental Concerns The spread of oil leaking from a tanker is i...
 6.1.69: Production Cost The price p, in dollars, of a certain product and t...
 6.1.70: Cost of a Commodity The price p, in dollars, of a certain commodity...
 6.1.71: Volume of a Cylinder The volume V of a right circular cylinder of h...
 6.1.72: Volume of a Cone The volume V of a right circular cone is If the he...
 6.1.73: Foreign Exchange Traders often buy foreign currency in hope of maki...
 6.1.74: Temperature Conversion The function converts a temperature in degre...
 6.1.75: Discounts The manufacturer of a computer is offering two discounts ...
 6.1.76: If and are odd functions, show that the composite function is also ...
 6.1.77: If is an odd function and is an even function, show that the compos...
Solutions for Chapter 6.1: Algebra and Trigonometry 9th Edition
Full solutions for Algebra and Trigonometry  9th Edition
ISBN: 9780321716569
Solutions for Chapter 6.1
Get Full SolutionsAlgebra and Trigonometry was written by and is associated to the ISBN: 9780321716569. This expansive textbook survival guide covers the following chapters and their solutions. Since 77 problems in chapter 6.1 have been answered, more than 61429 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 9. Chapter 6.1 includes 77 full stepbystep solutions.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

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

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.

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.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

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

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

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].

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.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

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

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

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.

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

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

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