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Chapter 5: Q. 37 (page 257)

In Problems 29 鈥� 44, for the given functions f and g, find:

(a)fog

(b) gof

(c) fof

(d) gog

State the domain of each composite function.

f(x)=xx-1g(x)=-4x

Short Answer

Expert verified

a)f鈭�g=44+xand its domain is:{x|x鈮�0,x鈮�-4}

b) g鈭�f=-4(x-1)x, and its domain:x|x鈮�1,x鈮�0

c)f鈭�f=x and its domain is:x|x鈮�1.

d)g鈭�g=xand its domain is:x|x鈮�0

Step by step solution

01

Step 1. Given information:

The functions are:

f(x)=xx-1g(x)=-4x

The domain of f(x)is: {x|x鈮�1}

The domain ofg(x)is:{x|x鈮�0}

02

Part (a)  Step 1. To find f ∘g and its domain:

f鈭�g(x)=f(g(x))=-4x-4x-1=-4-4-x=44+x

The domain off鈭�gis:{x|x鈮�-4,x鈮�0}

03

Part (b)  Step 1. To find g∘ f and its domain:

g鈭�f=g(f(x))=-4xx-1=-4(x-1)x

The domain of g鈭�fis: x|x鈮�0,x鈮�1.

04

Part (c)  Step 1. To find f∘f and its domain:

f鈭�f=f(f(x))=xx-1xx-1-1=xx-1x-x+1x-1=xx-1脳x-11=x

Its domain is:x|x鈮�1

05

Part (c)  Step 1. To find g∘g and its domain:

g鈭�g=-4-4x=x

its domain is:x|x鈮�0

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Most popular questions from this chapter

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

A(n)________ is a function of the form f(x)=Caxwhere a>0,a鈮�1,and C鈮�0are real numbers. The base ais a ____ and C is a _____.

If f(x)=ax+band g(x)=cx+d, then find: -

(a)f鈭�g

(b)g鈭�f

(c)the domain of f鈭�gand g鈭�f

(d)the conditions for whichf鈭�g=g鈭�f

Iffx=ax, show thatfx+h-fxh=ax.ah-1hh鈮�0.

solve each equation

92x27x2=3-1

solve each equation. Verify your results using a graphing utility.

ex=e3x+8
See all solutions

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