Download the App!

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

If $ f(x) = 3x^2 - x + 2 $ , find $ f(2) $ , $ f(-2) $ , $ f(a) $ , $ f(-a) $ , $ f(a + 1) $ , 2 $ f(a) $ , $ f(2a) $ , $ f(a^2) $ , $ [ f(a) ]^2 $ , and $ f(a + h) $.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$f(x)=3 x^{2}-x+2$$f(2)=3(2)^{2}-2+2=12-2+2=12$$f(-2)=3(-2)^{2}-(-2)+2=12+2+2=16$$f(a)=3 a^{2}-a+2$$f(-a)=3(-a)^{2}-(-a)+2=3 a^{2}+a+2$$f(a+1)=3(a+1)^{2}-(a+1)+2=3\left(a^{2}+2 a+1\right)-a-1+2=3 a^{2}+6 a+3-a+1=3 a^{2}+5 a+4$$2 f(a)=2 \cdot f(a)=2\left(3 a^{2}-a+2\right)=6 a^{2}-2 a+4$$f(2 a)=3(2 a)^{2}-(2 a)+2=3\left(4 a^{2}\right)-2 a+2=12 a^{2}-2 a+2$$f\left(a^{2}\right)=3\left(a^{2}\right)^{2}-\left(a^{2}\right)+2=3\left(a^{4}\right)-a^{2}+2=3 a^{4}-a^{2}+2$$\begin{aligned}[f(a)]^{2} &=\left[3 a^{2}-a+2\right]^{2}=\left(3 a^{2}-a+2\right)\left(3 a^{2}-a+2\right) \\ &=9 a^{4}-3 a^{3}+6 a^{2}-3 a^{3}+a^{2}-2 a+6 a^{2}-2 a+4=9 a^{4}-6 a^{3}+13 a^{2}-4 a+4 \\ f(a+h) &=3(a+h)^{2}-(a+h)+2=3\left(a^{2}+2 a h+h^{2}\right)-a-h+2=3 a^{2}+6 a h+3 h^{2}-a-h+2 \end{aligned}$

21:52

Albina Emelina

06:30

Heather Zimmers

Calculus 1 / AB

Calculus 2 / BC

Calculus 3

Chapter 1

Functions and Models

Section 1

Four Ways to Represent a Function

Functions

Integration Techniques

Partial Derivatives

Functions of Several Variables

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

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.

08:09

If $ f(x) = 3x^2 - x + 2 $…

12:14

If $f(x)=3 x^{2}-x+2$, fin…

0:00

If $f(x)=3 x^{2}-x+2$ find…

09:53

If $f(x)=3 x^{2}-x+2,$ fin…

03:11

If $F(x)=x^{2}+3 x+2,$ fin…

01:08

If $f(x)=2 x^{2}-x-1,$ fin…

01:12

If $f(x)=x^{2}-2 x,$ find …

01:46

If $f(x)=x^{3}+x^{2}-x-1,$…

01:29

$$\text { If } f(x)=x^…

Alright today we'll have some fun with functions. All right, so here we have F. Of X equal to three X squared minus X plus two. And we're just gonna plug in a lot of different values and do some manipulation just to kind of practice working with function. So let's take a look at um effort to that. Just means you substitute two for every value of X. So replace X by two and we have to do order of operations. So it's three times four. We do the two squared first -2 plus two. So we get 12 And then -2-plus 2 cancels. So we get just 12. So f of two is 12. No f of -2. We can plug in for acts. We just have to be careful with that minus sign and notice we have some double negatives and so forth. So we've got to just be super careful In order of operations will do the squared first a -2 times a -2 is a positive four. So three times positive four. But here we're gonna get plus. Oops, I forgot to plug in. Um Oh I just made a mistake. They should just say -2. Let's fix that. Okay so then we get um plus two plus two because that double negative so we get 12 plus four Or 16. So notice that you have to be very careful, it made a difference between plugging into and plugging in a -2. Now we'll do the same thing but we're going to plug in A. So we'll get three A squared minus A. Plus two. So that is done for minus A. We're going to be super careful again with that minus sign and see what happens. The minus eight times minus A. Is a positive A. Squared. So we get three A squared Plus a plus two and so you can see that it looks different so you have to be super careful with that minus sign. Now let's go ahead and plug in a plus one. So we get three times a plus one Squared minus parentheses a plus one Plus two. If we clean that up then we would um multiply eight plus one times A plus one. So a squared plus two A. Plus one and we'll distribute the minus sign. So you can see there's a lot of careful work that has to be done so that gives us three A squared plus six A. Plus three. When I distribute the three to that big parentheses e then I get minus A. And then minus one plus two is just plus one so I'm gonna try to make sure I have room for it. So we'll switch colors for the next problem so if we combine terms we get three A squared Plus five A. Plus four. Um Okay so that is our answer for that one for the others. I'll go ahead and circle the answers as well. Okay excellent. Okay so the next one is um this is gonna be a different color. Okay the next one is twice F. Of A. So it's just twice X. Replaced with A. And we can distribute so we'll get six A squared minus to a plus four. Alright so that is our answer for that one. We're getting there step by step. Okay now we have F. Of a squared. That means every X gets replaced by a squared but we still have to square it minus a squared plus two. So we do the power first. So we get a squared squared is eight of the fourth. So we get 38 of the fourth minus a squared plus two. And that's complete. Alright so now the next one is gonna be um we have to do kind of a triple foil. So we have F. F. A. Is 38 squared minus a plus two. But now we need to square it so we have to multiply every term by itself. Um So basically I'm gonna multiply this term by every term and distribute. So that gives me 98 of the 4th -3 A Square. No a cute. Um Plus six A squared. Next I'm going to multiply the middle term by every term. So that will give me -3 a. q. Plus a squared minus two A. And finally we will take the last term which is a two and multiplied by every term. So it gives me plus six A squared minus to a plus four. All right look at that. So now we'll try to clean this up I'll just try to kind of do it down here so we'll get 98 of the four. So that took care of this term. We've got how many a cubes -3 and another -3. So that's -6 a cube. Let's see for a squares we have a six The ones that makes seven plus 6 13 A squared. Let's see just as -2 and -2. So -4 a. Plus four wow okay a lot of work for that guy. Okay one last left and we're going to just substitute A. Plus H. Into our um X. Term and that's just substituting in. Um And if we want to clean it up we don't have to but if we want to it would be three times a squared plus two A. H. Just in a little foil there um minus a minus H distributing the minus one plus two. So it doesn't really clean up very nicely. It looks like we get three A squared plus six A. Eight um Plus three H. Squared. Oh everything is like its own term minus a minus H. Plus two. Okay so it doesn't clean up very nicely but there it is we solved all of them so hopefully that was a nice introduction to just working with the the functions with different inputs. Okay have a wonderful day

View More Answers From This Book

Find Another Textbook

01:39

Solve the following equation for b. Be sure to take into account whether a l…

03:19

Daria is sticking premade 2 foot by 2 foot carpet squares to her office floo…

02:12

Use the graph to estimate the X- and y-intercepts of this function and descr…

01:09

Estimate the answer to 738 + 577 by rounding each number to the nearest hund…

01:31

For what values of x and y are the triangles to the right congruent by HL?

02:32

Given the following system of equations in matrix form with matrix A [:&…

02:36

A client asked Leah to design a rectangular garden with a length that is two…

a) What is the x-coordinate of every point along this line?b) Use your a…

01:18

a) What is the size of angle ABC?b) Use your answer to part a) to work o…

02:17

Identify two angles that are marked congruent to each other on the 'dia…