/*! 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} Problem 110 Use the functions \(f(x)=\frac{1... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 110

Use the functions \(f(x)=\frac{1}{8} x-3\) and \(g(x)=x^{3}\) to find the indicated value or function. $$g^{-1} \circ f^{-1}$$

Short Answer

Expert verified
The composite function \(g^{-1} \circ f^{-1}\) is \(\sqrt[3]{8x+24}\)

Step by step solution

01

Find the Inverse of f

To find the inverse of a function, you should switch \(y\) (or \(f(x)\)) with \(x\). Here, \(f(x)=\frac{1}{8}x-3\) becomes \(x = \frac{1}{8}y - 3\). Solving for \(y\) gives \(f^{-1}(x) = 8x + 24\).
02

Find the Inverse of g

Applying the same process to the function \(g\), we get \(x = y^{3}\). To get the inverse function, we solve for \(y\), giving \(y = \sqrt[3]{x}\). So \(g^{-1}(x) = \sqrt[3]{x}\).
03

Find the Composite Function

Now we need to form the composite function \(g^{-1} \circ f^{-1}\) by substituting \(f^{-1}(x)\) into \(g^{-1}(x)\). We get \(g^{-1}(f^{-1}(x))= \sqrt[3]{8x+24}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Determine whether the statement is true or false. Justify your answer. It is possible for an odd function to have the interval \([0, \infty)\) as its domain.

Use the fact that the graph of \(y=f(x)\) has \(x\) -intercepts at \(x=2\) and \(x=-3\) to find the \(x\) -intercepts of the given graph. If not possible, state the reason.$$y=f(-x)$$.

Find the domain of the function.$$f(x)=\sqrt{100-x^{2}}$$.

Use the fact that the graph of \(y=f(x)\) has \(x\) -intercepts at \(x=2\) and \(x=-3\) to find the \(x\) -intercepts of the given graph. If not possible, state the reason.$$y=f(x-3)$$.

(a) use a graphing utility to graph the function \(f,\) (b) use the draw inverse feature of the graphing utility to draw the inverse relation of the function, and (c) determine whether the inverse relation is an inverse function. Explain your reasoning. $$f(x)=\frac{4 x}{\sqrt{x^{2}+15}}$$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.