Question

What is (f-g)(x)

f(x)= x^3-2x^2+12x-6
g(x)= 4x^2-6x+4

Enter your answer in standard form in the box.

(f-g)(x)=

Answer 1

Another way to write that is

(f - g)(x) = f(x) - g(x)

Answer 2

So

(x^3-2x^2+12x-6) - (4x^2-6x+4)

First we have to distribute the negative inside the parenthesis, can you do that?

Answer 3

I'm so lost lmao

Answer 4

better way to ask
do you know how to add/subtract polynomials?

Answer 5

No not really

Answer 6

oop

Answer 7

My brain is legit fried rn I've been at work all day and coming home to do schoolwork is not my favorite thing to do especially MATH.

Answer 8

well, then thank @AZ for being here lol

Answer 9

let me show you an example with some simpler numbers

if we have two functions, one is called f and another is called g

f(x) = x + 2
g(x) = 2x + 3

and they want us to find (f-g)(x)

as I said earlier
(f-g)(x) is the same thing as f(x) - g(x)

so that would be
(x+2) - (2x+3)

we have to distribute the minus inside which means we flip the signs inside and we'd get

x + 2 - 2x - 3

and then we can simplify it

Answer 10

Thank yall both for helping me

Answer 11

ah, yes
doing math after a long day is no fun

I'm not sure if you've read my example so far, but it's fine if you didn't

let's take it step by step

Answer 12

Okay thank you, i'm reading it now

Answer 13

So we said we had to do

\(\color{red}{f(x)} - \color{orange}{g(x)}\)

and we took that huge chunk of letters and numbers and put them in their place and got

\(\color{red}{(x^3-2x^2+12x-6)} - \color{orange}{(4x^2-6x+4)}\)

but let's look at it one part at a time

I added colors so you could see which part is f(x) and which one is g(x) and not get confused because there's so many letters and numbers everywhere

Answer 14

Thanks lol.

Answer 15

the first step we have to do is- distribute the negative sign inside of the parenthesis

so let's only look at the right half that's in orange

\(- (4x^2 - 6x + 4)\)

do you know how to multiply that negative sign inside?

as a hint using some other letters
-(a + b - c)
= -a - b + c

do you see how the signs in front of each variable (or letter) changes?

Answer 16

yeah

Answer 17

good! so can you similarly do that for

−(4x^2 − 6x + 4)

Answer 18

ok

Answer 19

4x^2 is positive so it's going to become -4x^2 when we bring that - inside the parenthesis

what's the opposite of the minus sign?
is it a + sign?

and for the third one- what's the opposite of the plus sign