Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Problem 1

Find \(f(g(x))\) when \(f(x)=x-7\) and \(g(x)=x^{2}\).

Short Answer

Expert verified
Answer: The composition of the functions, \(f(g(x))=x^{2}-7\).

Step by step solution

01

Write the given functions

The functions we are given are \(f(x)=x-7\) and \(g(x)=x^{2}\).
02

Evaluate \(g(x)\)

Since we are finding \(f(g(x))\), first we need to evaluate \(g(x)\). We have \(g(x)=x^{2}\).
03

Substitute \(g(x)\) in \(f(x)\)

Now we need to substitute the result of \(g(x)\) in the function \(f(x)\). So, we have \(f(g(x)) = f(x^{2})\).
04

Evaluate \(f(g(x))\)

Substitute \(x^{2}\) into \(f(x)\): \(f(g(x)) = f(x^{2}) = x^{2}-7\). So, the composition of the functions \(f(x)\) and \(g(x)\), \(f(g(x))=x^{2}-7\).

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

By sketching a graph of \(y=3 x-1\) show that this is a one-to-one function.

If \(f(x)=x+6\) and \(g(x)=x^{2}-5\) find (a) \(f(g(0))\), (b) \(g(f(0))\), (c) \(g(g(2))\), (d) \(f(g(7))\).

Plot a graph of the following functions. In each case state the domain and the range of the function. (a) \(f(x)=3 x+2,-2 \leq x \leq 5\) (b) \(g(x)=x^{2}+4,-2 \leq x \leq 3\) (c) \(p(t)=2 t^{2}+8,-2 \leq t \leq 4\) (d) \(f(t)=6-t^{2}, 1 \leq t \leq 5\)

Explain what is meant by a function.

Given the function \(g(t)=8 t+3\) find (a) \(g(7)\) (b) \(g(2)\) (c) \(g(-0.5)\) (d) \(g(-0.11)\)
See all solutions

Recommended explanations on Physics Textbooks

Rotational Dynamics

Read Explanation

Force

Read Explanation

Electric Charge Field and Potential

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Dynamics

Read Explanation

Thermodynamics

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.

Sign-up for free