/*! 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 97 Find a formula for the inverse f... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 97

Find a formula for the inverse function \(f^{-1}\) of the indicated function \(f\). $$ f(x)=4 x^{3 / 7}-1 $$

Short Answer

Expert verified
The inverse function of \(f(x) = 4x^{3/7} - 1\) is \(f^{-1}(x) = \left(\frac{x + 1}{4}\right)^{7/3}\).

Step by step solution

01

Rewrite the function using y

Rewrite the given function with \(y\) instead of \(f(x)\): $$ y = 4x^{3/7} - 1 $$
02

Swap x and y variables

Swap the \(x\) and \(y\) variables in the equation: $$ x = 4y^{3/7} - 1 $$
03

Solve for y in terms of x

To solve for \(y\), follow these steps: 1. Add \(1\) to both sides of the equation: $$ x + 1 = 4y^{3/7} $$ 2. Divide both sides by \(4\): $$ \frac{x + 1}{4} = y^{3/7} $$ 3. Raise both sides to the power of \(7/3\) to eliminate the exponent on \(y\): $$ \left(\frac{x + 1}{4}\right)^{7/3} = y $$ Now, we have found the inverse function: $$ f^{-1}(x) = \left(\frac{x + 1}{4}\right)^{7/3} $$

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

Write each expression as the sum of a polynomial and a rational function whose numerator has smaller degree than its denominator. $$ \frac{x^{2}}{4 x+3} $$

Find a number \(b\) such that 3 is a zero of the polynomial \(p\) defined by $$ p(x)=1-4 x+b x^{2}+2 x^{3} $$.

Write the indicated expression as a ratio of polynomials, assuming that $$ r(x)=\frac{3 x+4}{x^{2}+1}, \quad s(x)=\frac{x^{2}+2}{2 x-1}, \quad t(x)=\frac{5}{4 x^{3}+3} $$. $$ \frac{s(1+x)-s(1)}{x} $$

Show that if \(p\) and \(q\) are nonzero polynomials with \(\operatorname{deg} p<\operatorname{deg} q,\) then \(\operatorname{deg}(p+q)=\operatorname{deg} q\).

Write the domain of the given function \(r\) as a union of intervals. $$ r(x)=\frac{4 x^{7}+8 x^{2}-1}{x^{2}-2 x-6} $$
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Mechanics Maths

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.