/*! 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 117 Determine whether each statement... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 117

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If \(f(x)=\sqrt{x}\) and \(g(x)=2 x-1,\) then \((f \circ g)(5)=g(2)\)

Short Answer

Expert verified
The statement is True. The value of both \((f \circ g)(5)\) and \(g(2)\) are equal to 3.

Step by step solution

01

Define the Functions

The two functions that we are given are \(f(x)=\sqrt{x}\) and \(g(x)=2 x-1\)
02

Calculate \(f \circ g\)(5)

The statement \((f \circ g)(5) = g(2)\) implies that you have to calculate \(f(g(5))\). Plug the value 5 into the function g, we get \(g(5)=2\cdot 5-1 = 9\). Then plug this result into the function f. The result is \(f(g(5))=\sqrt{9}=3\)
03

Calculate g(2)

Next, calculate the value of g at 2. By substituting 2 into g, we get \(g(2)=2\cdot 2-1 = 3\).
04

Compare the Results

The final comparison between \(f(g(5))\) and \(g(2)\) shows that they both equal 3, which means the given statement is true.

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

Solve for \(y: \quad x=y^{2}-1, y \geq 0\)

Express the given function \(h\) as \(a\) composition of two functions \(f\) and \(g\) so that \(h(x)=(f \circ g)(x)\). $$h(x)=\frac{1}{4 x+5}$$

Find a. \((f \circ g)(x)\) b. \((g \circ f)(x)\) c. \((f \circ g)(2)\) d. \((g \circ f)(2)\) $$f(x)=7 x+1, g(x)=2 x^{2}-9$$

Express the given function \(h\) as \(a\) composition of two functions \(f\) and \(g\) so that \(h(x)=(f \circ g)(x)\). $$h(x)=(2 x-5)^{3}$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ \begin{aligned} &\text { If } f(x)=x^{2}-4 \text { and } g(x)=\sqrt{x^{2}-4}, \text { then }(f \circ g)(x)=-x^{2}\\\ &\text { and }(f \circ g)(5)=-25 \end{aligned} $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Pure 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.