Answered: Consider the functions f(x)= x³ - 5 and…

Consider the functions f(x)= x³ - 5 and g(x)=³√x+5. (a) Find f(g(x)). (b) Find g(f(x)). (c) Determine whether the functions f and g are inverses of each other.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.7: Inverse Functions

Problem 2SE: Why do we restrict the domain of the function f(x)=x2 to find the function's inverse?

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Question

3
Consider the functions f(x) = x³ - 5 and g(x)=√x+5.
(a) Find f(g(x)).
(b) Find g(f(x)).
(c) Determine whether the functions f and g are inverses of each other.

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Step 2: We have solve for f(g(x)) and g(f(x)) .

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Step 3: since f(g(x)) = g(f(x)) = x so f(x) and g(x) are inverse to each to each other

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