/*! 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 90 Find a formula for the inverse f... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 90

Find a formula for the inverse function \(f^{-1}\) of the indicated function \(f\). $$ f(x)=x^{1 / 11} $$

Short Answer

Expert verified
The inverse function of the given function \(f(x) = x^{1/11}\) is \(f^{-1}(x) = x^{11}\).

Step by step solution

01

Replace \(f(x)\) with \(y\)

We replace \(f(x)\) with \(y\) to rewrite the function in terms of \(y\): $$ y = x^{1/11} $$
02

Swap \(x\) and \(y\)

Swapping \(x\) and \(y\) in the equation, as we want to find the inverse function, we get: $$ x = y^{1/11} $$
03

Solve for \(y\)

To solve for \(y\), we will raise both sides of the equation to the power of 11, as we want to eliminate the exponent \(1/11\) in the equation. So, $$ x^{11} = (y^{1/11})^{11} $$ Simplifying the right side, we obtain: $$ x^{11} = y $$
04

Write the final result

The final result should be written as a function of \(x\). The inverse function of \(f(x)\), denoted by \(f^{-1}(x)\), is: $$ f^{-1}(x) = x^{11} $$

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 the indicated expression as \(a\) polynomial. $$ \frac{q(2+x)-q(2)}{x} $$

Sketch the graph of the given function \(f\) on the interval [-1.3,1.3]. $$ f(x)=-3 x^{3} $$

$$ \text { Suppose } p(x)=2 x^{6}+3 x^{5}+5 $$ (a) Show that if \(\frac{M}{N}\) is a zero of \(p\), then $$ 2 M^{6}+3 M^{5} N+5 N^{6}=0 $$ (b) Show that if \(M\) and \(N\) are integers with no common factors and \(\frac{M}{N}\) is a zero of \(p\), then \(5 / M\) and \(2 / N\) are integers. (c) Show that the only possible rational zeros of \(p\) $$ \text { are }-5,-1,-\frac{1}{2}, \text { and }-\frac{5}{2} \text { . } $$ (d) Show that no rational number is a zero of \(p\).

Find a polynomial \(p\) of degree 3 such that \(-2,-1,\) and 4 are zeros of \(p\) and \(p(1)=2\).

Write each expression as the sum of a polynomial and a rational function whose numerator has smaller degree than its denominator. $$ \frac{4 x-5}{x+7} $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

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.