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Chapter 6: Q. 45 (page 419)

find (f∘g)(x)and(g∘f)(x)and graph each of these functions.

localid="1646342074607" role="math" f(x)=tanxg(x)=4x

Short Answer

Expert verified

If f(x)=tanxand g(x)=4xthen(f∘g)(x)=tan(4x)and its graph is

and (g∘f)(x)=4tan(x)and its graph is

Step by step solution

01

Step 1. Given data

The given functions are

f(x)=tanxg(x)=4x

02

Step 2. Composition of function

(f∘g)(x)composition of function is

(f∘g)(x)=f(g(x))(f∘g)(x)=f(4x)(f∘g)(x)=tan(4x)

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

03

Step 3. Graph of (f∘g)(x)

Plot the points of(f∘g)(x)=tan(4x)and connect them smoothly

04

Step 4. Composition of function

(g∘f)(x)Composition of function is

(g∘f)(x)=g(f(x))(g∘f)(x)=g(tan(x))(g∘f)(x)=4tan(x)

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

05

Step 5. Graph of (g∘f)(x)

Plot the points of(g∘f)(x)=4tan(x) and connect them smoothly

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