/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 47 find (f鈭榞)(x)and(g鈭榝)(x) and... [FREE SOLUTION] | 91影视

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Chapter 6: Q. 47 (page 419)

find (f鈭�g)(x)and(g鈭�f)(x) and graph each of these functions.
role="math" localid="1646344152688" f(x)=-2xg(x)=cotx

Short Answer

Expert verified

If f(x)=-2xand g(x)=cotxthen(f鈭�g)(x)=-2cot(x)and its graph is

and (g鈭�f)(x)=cot(-2x)and its graph is

Step by step solution

01

Step 1. Given data

The given functions are

f(x)=-2xg(x)=cotx

02

Step 2. Composition of function 

(f鈭�g)(x)composition of function is

role="math" localid="1646344262300" (f鈭�g)(x)=f(g(x))(f鈭�g)(x)=f(cot(x))(f鈭�g)(x)=-2(cot(x))(f鈭�g)(x)=-2cot(x)

03

Step 3. Graph of (f∘g)(x)

Plot the graph of (f鈭�g)(x)=-2cot(x)

04

Step 4. Composition of function 

(g鈭�f)(x)composition of function is

role="math" localid="1646344376679" (g鈭�f)(x)=g(f(x))(g鈭�f)(x)=g(-2x)(g鈭�f)(x)=cot(-2x)

Consider different values of x and determine the coordinate of several points

05

Step 5. Graph of (g∘f)(x)

Plot the graph of(g鈭�f)(x)=cot(-2x)

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