/*! 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 25 Find a formula for the inverse f... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 25

Find a formula for the inverse function \(f^{-1}\) of the indicated function \(f\). $$ f(x)=x^{-2 / 5} $$

Short Answer

Expert verified
The inverse function of \(f(x) = x^{-\frac{2}{5}}\) is \(f^{-1}(x) = x^{-\frac{5}{2}}\).

Step by step solution

01

Write the function in terms of y

Write the given function \(f(x) = x^{-2/5}\) as \(y = x^{-2/5}\).
02

Swap x and y

Swap \(x\) and \(y\) so that we can find the inverse function in terms of \(x\). After swapping, the equation will be \(x = y^{-2/5}\).
03

Solve for y

To solve for \(y\), first raise both sides to the power of \(-5/2\) to remove the exponent on the right-hand side: \[ (x^{-1})^{\frac{-5}{2}}=y^{\frac{-5}{2}\cdot\frac{-2}{5}} \\ \implies x^{\frac{-5}{2}}=y \]
04

Simplify the expression

The expression is already simplified to \(y=x^{-\frac{5}{2}}\), and this is the formula for the inverse function. Therefore, the inverse function is \(f^{-1}(x) = x^{-\frac{5}{2}}\).

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

Show that \(\sqrt{2-\sqrt{3}}=\sqrt{\frac{3}{2}}-\sqrt{\frac{1}{2}}\).

Is the function \(f\) defined by \(f(x)=2^{x}\) for every real number \(x\) an even function, an odd function, or neither?

Find all numbers \(x\) that satisfy the given equation. $$ (\log (6 x)) \log x=5 $$

Explain how you would use a calculator to verify that $$ 2^{13746}<13746^{1000} $$ but $$ 2^{13747}>13747^{1000} $$ and then actually use a calculator to verify both these inequalities. [The numbers involved in these inequalities have over four thousand digits. Thus some cleverness in using your calculator is required.]

Show that an earthquake with Richter magnitude \(R\) has seismic waves of size \(S_{0} 10^{R},\) where \(S_{0}\) is the size of the seismic waves of an earthquake with Richter magnitude \(0 .\)
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

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.