Let $ f(x) = (x-1)^{\frac{3}{2}} $, $ g(x) = x^2 $, and $ E = \{x: -8 \leq x \leq 8\} $. Find the inverse image $(g \circ f)^{-1}(E)$.

The given functions and .The aim is to find the inverse image of .

Answered: Let_f(x)=(x-1)², g(x)=x², and E=…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Let $ f(x) = (x-1)^{\frac{3}{2}} $, $ g(x) = x^2 $, and $ E = \{x: -8 \leq x \leq 8\} $. Find the inverse image $(g \circ f)^{-1}(E)$.

Expert Solution

Step 1: Given the information

The given functions $f open parentheses x close parentheses equals open parentheses x minus 1 close parentheses to the power of 3 over 2 end exponent comma space g open parentheses x close parentheses equals x squared comma$ and $E equals open curly brackets x vertical line space minus 8 less or equal than x less or equal than 8 close curly brackets$ .

The aim is to find the inverse image of $open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses E close parentheses$ .