Precalculus: Graphical, Numerical, Algebraic 8th Edition solutions

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, find the domain of the function and express it in interval notation \(f(x)=\frac{x-2}{x+3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, find the domain of the function and express it in interval notation \(g(x)=\ln (x-1)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, find the domain of the function and express it in interval notation \(f(t)=\sqrt{5-t}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, find the domain of the function and express it in interval notation \(g(x)=\frac{3}{\sqrt{2 x-1}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, find the domain of the function and express it in interval notation \(f(x)=\sqrt{\ln (x)}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, find the domain of the function and express it in interval notation \(h(x)=\sqrt{1-x^{2}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, find the domain of the function and express it in interval notation \(f(t)=\frac{t+5}{t^{2}+1}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, find the domain of the function and express it in interval notation \(g(t)=\ln (|t|)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, find the domain of the function and express it in interval notation \(f(x)=\frac{1}{\sqrt{1-x^{2}}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-10, find the domain of the function and express it in interval notation g(x) = 2

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-4, find formulas for the functions f + g, f - g and fg. Give the domain of each. \(f(x)=2 x-1 ; g(x)=x^{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-4, find formulas for the functions f + g, f - g and fg. Give the domain of each. \(f(x)=(x-1)^{2} ; g(x)=3-x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-4, find formulas for the functions f + g, f - g and fg. Give the domain of each. \(f(x)=\sqrt{x} ; g(x)=\sin x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 1-4, find formulas for the functions f + g, f - g and fg. Give the domain of each. \(f(x)=\sqrt{x+5} ; g(x)=|x+3|\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5-8, find formulas for f/g and g/f. Give the domain of each. \(f(x)=\sqrt{x+3} ; g(x)=x^{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5-8, find formulas for f/g and g/f. Give the domain of each. \(f(x)=\sqrt{x-2} ; g(x)=\sqrt{x+4}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5-8, find formulas for f/g and g/f. Give the domain of each. \(f(x)=x^{2} ; g(x)=\sqrt{1-x^{2}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 5-8, find formulas for f/g and g/f. Give the domain of each. \(f(x)=x^{3} ; g(x)=\sqrt[3]{1-x^{3}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
\(f(x)=x^{2}\) and g(x) = 1/x are shown below in the viewing window [0, 5] by [0, 5]. Sketch the graph of the sum (f+g)(x) by adding the y-coordinates directly from the graphs. Then graph the sum on your calculator and see how close you came.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
The graphs of \(f(x)=x^{2}\) and g(x) = 4 - 3x are shown in the viewing window [-5,5] by [-10,25] Sketch the graph of the difference (f-g)(x) by subtracting the y-coordinates directly from the graphs. Then graph the difference on your calculator and see how close you came.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-14, find \((f \circ g)(3) \text { and }(g \circ f)(-2)\) \(f(x)=2 x-3 ; g(x)=x+1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-14, find \((f \circ g)(3) \text { and }(g \circ f)(-2)\) \(f(x)=x^{2}-1 ; g(x)=2 x-3\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-14, find \((f \circ g)(3) \text { and }(g \circ f)(-2)\) \(f(x)=x^{2}+4 ; g(x)=\sqrt{x+1}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 11-14, find \((f \circ g)(3) \text { and }(g \circ f)(-2)\) \(f(x)=\frac{x}{x+1} ; g(x)=9-x^{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 15-22, find \(f(g(x)) \text { and } g(f(x))\). State the domain of each. \(f(x)=3 x+2 ; g(x)=x-1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 15-22, find \(f(g(x)) \text { and } g(f(x))\). State the domain of each. \(f(x)=x^{2}-1 ; g(x)=\frac{1}{x-1}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 15-22, find \(f(g(x)) \text { and } g(f(x))\). State the domain of each. \(f(x)=x^{2}-2 ; g(x)=\sqrt{x+1}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 15-22, find \(f(g(x)) \text { and } g(f(x))\). State the domain of each. \(f(x)=\frac{1}{x-1} ; g(x)=\sqrt{x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 15-22, find \(f(g(x)) \text { and } g(f(x))\). State the domain of each. \(f(x)=x^{2} ; g(x)=\sqrt{1-x^{2}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 15-22, find \(f(g(x)) \text { and } g(f(x))\). State the domain of each. \(f(x)=x^{3} ; g(x)=\sqrt[3]{1-x^{3}}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 15-22, find \(f(g(x)) \text { and } g(f(x))\). State the domain of each. \(f(x)=\frac{1}{2 x} ; g(x)=\frac{1}{3 x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 15-22, find \(f(g(x)) \text { and } g(f(x))\). State the domain of each. \(f(x)=\frac{1}{x+1} ; g(x)=\frac{1}{x-1}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 23-30, find (x) and g(x) so that the function can be described as y = f(g(x)). (There may be more than one possible decomposition.) \(y=\sqrt{x^{2}-5 x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 23-30, find (x) and g(x) so that the function can be described as y = f(g(x)). (There may be more than one possible decomposition.) \(y=\left(x^{3}+1\right)^{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 23-30, find (x) and g(x) so that the function can be described as y = f(g(x)). (There may be more than one possible decomposition.) \(y=|3 x-2|\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 23-30, find (x) and g(x) so that the function can be described as y = f(g(x)). (There may be more than one possible decomposition.) \(y=\frac{1}{x^{3}-5 x+3}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 23-30, find (x) and g(x) so that the function can be described as y = f(g(x)). (There may be more than one possible decomposition.) \(y=(x-3)^{5}+2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 23-30, find (x) and g(x) so that the function can be described as y = f(g(x)). (There may be more than one possible decomposition.) \(y=e^{\sin x}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 23-30, find (x) and g(x) so that the function can be described as y = f(g(x)). (There may be more than one possible decomposition.) \(y=\cos (\sqrt{x})\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 23-30, find (x) and g(x) so that the function can be described as y = f(g(x)). (There may be more than one possible decomposition.) \(y=(\tan x)^{2}+1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Weather Balloons A high-altitude spherical weather balloon expands as it rises due to the drop in atmospheric pressure. Suppose that the radius r increases at the rate of 0.03 inch per second and that r = 48 inches at time t = 0. Determine an equation that models the volume V of the balloon at time t

Precalculus: Graphical, Numerical, Algebraic 8th Edition
A Snowballs Chance Jake stores a small cache of 4-inch-diameter snowballs in the basement freezer, unaware that the freezers self-defrosting feature will cause each snowball to lose about 1 cubic inch of volume every 40 days. He remembers them a year later (call it 360 days) and goes to retrieve them

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Satellite Photography A satellite camera takes a rectangle-shaped picture. The smallest region that can be photographed is a 5-km by 7-km rectangle. As the camera zooms out, the length l and width w of the rectangle increase at a rate of 2 km/sec. How long does it take for the area A to be at least 5

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Computer Imaging New Age Special Effects, Inc., prepares computer software based on specifications prepared by film directors. To simulate an approaching vehicle, they begin with a computer image of a 5-cm by 7-cm by 3-cm box. The program increases each dimension at a rate of 2 cm/sec. How long does

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which of the ordered pairs (1,1), (4,-2) and (3,-1) are in the relation given by 3x + 4y = 5?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which of the ordered pairs (5,1), (3,4) and (0,-5) are in the relation given by x2 + y2 = 25?

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 37-44, find two functions defined implicitly by the given relation. \(x^{2}+y^{2}=25\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 37-44, find two functions defined implicitly by the given relation. \(x+y^{2}=25\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 37-44, find two functions defined implicitly by the given relation. \(x^{2}-y^{2}=25\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 37-44, find two functions defined implicitly by the given relation. \(3 x^{2}-y^{2}=25\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 37-44, find two functions defined implicitly by the given relation. \(x+|y|=1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 37-44, find two functions defined implicitly by the given relation. \(x-|y|=1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 37-44, find two functions defined implicitly by the given relation. \(y^{2}=x^{2}\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
In Exercises 37-44, find two functions defined implicitly by the given relation. \(y^{2}=x\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
The domain of the quotient function (f/g)(x) consists of all numbers that belong to both the domain of and the domain of g. Justify your answer

Precalculus: Graphical, Numerical, Algebraic 8th Edition
The domain of the product function (g)(x) consists of all numbers that belong to either the domain of or the domain of g. Justify your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Suppose f and g are functions with domain all real numbers. Which of the following statements is not necessarily true? (A) \((f+g)(x)=(g+f)(x)\) (B) (f g)(x)=(g f)(x) (C) f(g(x))=g(f(x)) (D) (f-g)(x)=-(g-f)(x) (E) \((f \circ g)(x)=f(g(x))\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
If \(f(x)=x-7 \text { and } g(x)=\sqrt{4-x}\) , what is the domain of the function f/g? (A) \((-\infty, 4)\) (B) \((-\infty, 4]\) (C) \((4, \infty)\) (D) \([4, \infty)\) (E) \((4,7) \cup(7, \infty)\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Multiple Choice If \(f(x)=x^{2}+1, \text { then }(f \circ f)(x)=\) (A) \(2 x^{2}+2\) (B) \(2 x^{2}+1\) (C) \(x^{4}+1\) (D) \(x^{4}+2 x^{2}+1\) (E) \(x^{4}+2 x^{2}+2\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Which of the following relations defines the function y = |x| implicitly? (A) y = x (B) \(y^{2}=x^{2}\) (C) \(y^{3}=x^{3}\) (D) \(x^{2}+y^{2}=1\) (E) x = |y|

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Three on a Match Match each function f with a function g and a domain D so that \((f \circ g)(x)=x^{2}\) with domain D.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Be a g Whiz Let \(f(x)=x^{2}+1\). Find a function g so that (a) \((f g)(x)=x^{4}-1\) (b) \((f+g)(x)=3 x^{2}\) (c) \((f / g)(x)=1\) (d) \(f(g(x))=9 x^{4}+1\) (e) \(g(f(x))=9 x^{4}+1\)

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Identifying Identities An identity for a function operation is a function that combines with a given function f to return the same function f. Find the identity functions for the following operations: (a) Function addition. That is, find a function g such that (f+g)(x)=(g+f)(x)=f(x) (b) Func

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Is Function Composition Associative? You already know that function composition is not commutative; that is, \((f \circ g)(x) \neq(g \circ f)(x)\).But is function composition associative? That is, does \((f \circ(g \circ h))(x)=((f \circ g) \circ h))(x)\) Explain your answer.

Precalculus: Graphical, Numerical, Algebraic 8th Edition
Revisiting Example 6 Solve \(x^{2} y+y^{2}=5\) for y using the quadratic formula and graph the pair of implicit functions.