APP CAL MANAGE,LIFE,SOC STUD WEB ASSIGN
APP CAL MANAGE,LIFE,SOC STUD WEB ASSIGN
10th Edition
ISBN: 9781337825597
Author: Tan
Publisher: INTER CENG
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Chapter A, Problem 1E
To determine

To show: The function f and g are inverse of each other.

Expert Solution & Answer
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Explanation of Solution

Given:

The given functions are f(x)=13x3 , g(x)=3x3 .

Proof:

The domain and rang of the both functions are (,) .

Check the composition f[g(x)]=x .

f[g(x)]=f[3x3]=13(3x3)3=13(3x)313=13(3x)

That is, f[g(x)]=x .

Check the composition g[f(x)]=x .

g[f(x)]=g[(13x3)]=3(13x3)3=x33=x

That is, g[f(x)]=x .

Hence, the two functions f and g are inverse of each other is showed.

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Inverse Functions; Author: Professor Dave Explains;https://www.youtube.com/watch?v=9fJsrnE1go0;License: Standard YouTube License, CC-BY