Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

Use the given graphs of $ f $ and $ g $ to evaluate each expression, or explain why it is undefined.

(a) $ f (g(2)) $(b) $ g (f(0)) $(c) $ (f \circ g) (0) $(d) $ (g \circ f) (6) $(e) $ (g \circ g) (-2) $(f) $ (f \circ f) (4) $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Heather Zimmers

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

04:05

Jeffrey Payo

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 3

New Functions from Old Functions

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Missouri State University

Baylor University

University of Nottingham

Boston College

Lectures

04:31

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

0:00

Use the given graphs of $f…

02:30

13:39

02:27

02:26

05:34

Use the graphs of $f$ and …

00:24

Use the given graphs of f …

01:05

03:58

02:48

Use the graph to evaluate …

01:40

02:04

01:16

Use the graphs of $f(x)$ a…

02:47

all right. First, we're going to find part a f of G of two. So we start by finding g of to. So we find where X equals two. And then we follow that up to where it meets the G graph, and that would be at five. So g of two is five. We substitute that in, and now we're finding fo five. So we find X equals five and then we go up to where that meets the F graph, and that's at four. So our answer is for now we do something like that for part B. We start by finding f of zero. So we find X equals zero and we see where that matches the F graph, and that's at a height of zero. F of zero is zero. We substitute that in. Now we're finding g of zero. And so we go over to X equals zero and go up to where that meets the G graph. And that's at a height of three. Next, let's to part c f of g of zero. And we can write that this way if we want to f of g of zero. So the first thing we want to find is G of zero. So we go to where X equals zero and we find out on the G graph and that's three. Substitute that in, and now we have f of three. So we go over to where X equals three and we find that on the F graph, and that's at a height of zero. So the answer is zero. And now, for part D g of F six, that can be written as g of f of six like this. So the first thing we're finding his f of six. So we go over to where x equal six and we go up on the F graph and we get six for the height. So we substitute that in, and now we're finding g of six. However, six is not in the domain of G. It doesn't go that far, So this one is undefined. All right, here's part E. We can rewrite this as g of g of negative, too. And so on the inside, we're finding g of negative too. So we go over to where X equals negative to and find that on the G graph, and that's one so we substitute that in, and now we're finding g of one. So we go over to where X equals one, and we find that on the G graph. And that's right about four. So the answer is for and now for FFR four, which we can rewrite this way ff before we find the inside first effort for So we go over to where X equals four and we find that on the F graph. And that is it's supposed to be two minds a little low, but if you look at the actual graph, it's too. So we're going to substitute that in. And now we're looking for f of to. So we go to where X equals two and we find that on the F graph, and that is negative two. So there's our answer.

View More Answers From This Book

Find Another Textbook

02:11

Use the graph to determineopen intervals on which the function increasin…

01:22

Draw a Venn diagram like the following for each part Then shade each Venn di…

02:21

Find the measure of each angle 0 below: Round vour solutions to the nearest …

Suppose that an accelerating car goes from 0 mph to 65.5 mph in five seconds…

03:08

Exercise 1.39Let m and n be positive integers. By allowing the exponents…

00:53

Consider the level surface shown at theright: Match the slices with the …

Find an equation of the tangent line to the curve at the given point: Y = se…

04:40

About fifty- two percent of Americans use social media and other websites to…

06:33

client of a commercial rose grower has been keeping records on the shelf-lif…

01:32

Question 5pointNumber HelpA printed circuit board has 285 small …