/*! 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 16 Find \(f(g(x))\) and \(g(f(x))\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 16

Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=6 x \text { and } g(x)=\frac{x}{6}$$

Short Answer

Expert verified
Yes, the functions \(f(x) = 6x\) and \(g(x) = \frac{x}{6}\) are inverses of each other since \(f(g(x)) = x\) and \(g(f(x)) = x\).

Step by step solution

01

Compute \(f(g(x))\)

This is computed by substitution. Substitute \(g(x) = \frac{x}{6}\) into function \(f(x)\), in place of x. So, \(f(g(x)) = 6 * (\frac{x}{6}) = x\)
02

Compute \(g(f(x))\)

Similar to step 1, substitute \(f(x) = 6x\) into function \(g(x)\), in place of x. So, \(g(f(x)) = \frac{6x}{6} = x\
03

Compare \(f(g(x))\) and \(g(f(x))\) with x

Both of the evaluated results of \(f(g(x))\) and \(g(f(x))\) are equal to x. This means the functions \(f\) and \(g\) are inverses of each other

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

Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=-x \text { and } g(x)=x$$

The functions are all one-to-one. For each function, a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that \(f\left(f^{-1}(x)\right)=x\) and \(f^{-1}(f(x))=x\). $$f(x)=2 x$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If \((f+g)(a)=0,\) then \(f(a)\) and \(g(a)\) must be opposites, or additive inverses.

The functions are all one-to-one. For each function, a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that \(f\left(f^{-1}(x)\right)=x\) and \(f^{-1}(f(x))=x\). $$f(x)=4 x$$

Use a graphing utility to graph each function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). $$f(x)=|x-2|$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

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.