Question

I have a question and then later on maybe you could check my answer?

Answer 1

I need to find (2fg)(-1) where f(x) = 2x^2 + 5 and g(x) = -3x
What I'm planning on doing is this:
(-2x^2 - 5)(3x) but I don't know what to do with the 2 that was before the fg?

Answer 2

put the 2 infront of the whole equation

Answer 3

And once I do that, I multiply 2 times (-2x^2 - 5) and 2 times (3x)?

Answer 4

you multiply everything in the parentheses by 2..
2(-2x^2-5) 2(3x)
2*(-2)-2*(5)*2*(3) like this...

Answer 5

Okay!
Does the 2 become negative?
It's
(2)(-1)(2x^2 + 5)(-3x)

Answer 6

-1 is your x value

Answer 7

ohh right right okay one second

Answer 8

Okay I got -4x^2 - 10 - 6x
Is that correct? I multiplied everything by 2. Do I need to multiply -4x^2 - 10 by -6x?

Answer 9

now you need to substitute -1 in for every x

Answer 10

Okay

Answer 11

Wait I think I made a mistake, I multiplied everything by -1, one second

Answer 12

So I did
2(2x^2 + 5)(-3x)
4x^2 + 10 - 6x
4(-1)^2 + 10 - 6(-1)
4 + 10 - (-6)
= 20
Is that correct?

Answer 13

well 4* (-1)=-4 and then you would have to sqaure it
so it would be -4+10*(-6)

Answer 14

Oh, I thought you have to do -1^2 first

Answer 15

-64 then?

Answer 16

oops yea sorry you do do the -1^2 first

Answer 17

oh so then it is 20?

Answer 18

yea sorry

Answer 19

np

Answer 20

wait did you get that answer by subtracting -6 or multiplying it?

Answer 21

-6 should have been multiplied

Answer 22

oops I should be multiplying... ><

(4x^2 + 10)(-6x)
(4(-1)^2 + 10)(-6(-1))
(4 + 10)(6)
14 * 6 = 84

Answer 23

14*(-6)=-84

Answer 24

no but, it's -3x times 2 which is -6x and the x is -1 so (-6)(-1) equals 6?

Answer 25

oh sorry im doing 2 things at once your right its 84

Answer 26

(2fg)(-1) where f(x) = 2x^2 + 5 and g(x) = -3x
Are you sure we are not doing function composition,
which is written as \( 2 f \circ g \) ?

If not, then we interpret this to mean we multiply the two functions:
2 * f(x)*g(x)

we could do this the long way and get
2 * (2x^2 + 5) * (-3x) = -12x^3-30x
now we can find the value for any x, including x=-1
-12* (-1)^3 - 30 (-1) = 12+30= 42

the other way to do this is start with
2 * f(x)*g(x)

and replace x with -1:
2 * f(-1) * g(-1)
now find f(-1) = 2*(-1)^2 + 5 = 2+5= 7
and g(-1)= -3*-1= 3
now find
2 * 7 * 3= 42

Answer 27

That's how it was written, thanks Phi, thanks B. Sanders!