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
Find $ f \circ g \circ h $.
$ f(x) = \sqrt{x - 3} $ , $ g(x) = x^2 $ , $ h(x) = x^3 + 2 $
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
01:47
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
Oregon State University
Harvey Mudd College
University of Michigan - Ann Arbor
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.
00:56
$\text { Find } f \circ g …
00:43
Find $f \circ g \circ h$
00:55
Find $ f \circ g \circ h $…
02:27
Find $f(x)$ and $g(x)$ suc…
here we have functions F, g and H, and we're going to find the composition f of G of h. Another way to write that is with parentheses. F of G of age like this. So we can see from that that h of X is our innermost function and it's going to be substituted into G. And that means we're going to take a X cubed plus two and substituted in for X in the G function. And that gives us G of h of X equals X cubed plus two quantity squared. So that is G of h of X, and that whole thing gets substituted into the F function. So that whole thing goes in for X in the F function. And that's going to result in the square root of X cubed plus two quantity squared minus three. Now perhaps we want to simplify that. And if we do, we're going to end up squaring this X cubed plus two. We're going to multiply it out using the foil method, and that would give us X to the six power plus four X to the third power plus four and then we still have the minus three. So the last thing we want to do is combine the like terms and we have at the square root of X to the sixth power plus four x to the third power plus one.
View More Answers From This Book
Find Another Textbook
01:11
For an equation that represents as a function of $x$, the set of all values …
03:18
Match each function with its name.
$$f(x)=x$$
$$\begin{array…
01:20
A function value $f(a)$ is a relative _____ of $f$ if there exists an interv…
01:17
A graphical test for the existence of an inverse function of $f$ is called t…
01:46
The domain of $(f \circ g)$ is all $x$ in the domain of $g$ such that ______…
01:59
Plot the points in the Cartesian plane.$(-4,2),(-3,-6),(0,5),(1,-4)$
01:45
Plot the points in the Cartesian plane.$(0,0),(3,1),(-2,4),(1,-1)$
03:03
Use a graphing utility to graph the function. Be sure to choose an appropria…
02:54
Find the coordinates of the point.The point is located eight units below…
02:00
Find the coordinates of the point.The point is located five units below …