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Chapter 5: Q. 2 (page 348)

In Problems 2 鈥� 4, for the given functions f and g find:

(a) (f o g)(2)

(b) (g o f) (-2)

(c) (f o f)(4)

(d) ( g o g) (-1)

f(x)=3x-5;g(x)=1-2x2

Short Answer

Expert verified

(a) (f o g)(2)=-26

(b) (g o f) (-2) = -241

(c) (f o f)(4) = 16

(d) ( g o g) (-1) = -1

Step by step solution

01

Given Information 

We are given with two functions f(x) and g(x)

f(x)=3x-5;g(x)=1-2x2

02

Part(a) : Step 1: composition 

(fog)(2)=f(g(2))g(x)=1-2x2g(2)=1-2(2)2=-7f(-7)=3(-7)-5=-26(fog)(2)=f(g(2))=f(-7)=-26

03

Part(b) : Step 1: composition 

f(x)=3x-5;g(x)=1-2x2(gof)(-2)=g(f(-2))f(-2)=3(-2)-5=-11g(-11)=1-2(-11)2=-241(gof)(-2)=-241

04

Part(c) : Step 1: composition of functions

(fof)(4)=f(f(4))f(x)=3x-5f(4)=3(4)-5=7f(7)=3(7)-5=16(fof)(4)=16

05

Part(d) : Step 1: composition of functions

(gog)(-1)=g(g(-1))g(x)=1-2x2g(-1)=1-2(-1)2=-1(gog)(-1)=-1

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