Question

PLEASE HELP ME! I keep getting the wrong answer.

Given the parent functions f(x) = 5x − 1 and g(x) = 3x − 9, what is g(x) − f(x)?

g(x) − f(x) = 3x − 8 − 5x

g(x) − f(x) = 3x − 10 − 5x

g(x) − f(x) = −2x − 8 − 3x

g(x) − f(x) = −2x − 10 − 3x

Answer 1

What have you been trying so far?

Answer 2

My answer was the second one but i got that wrong.

Answer 3

I did 3^x-9-5x-1
my answer is 3^x-10-5x

Answer 4

I see. That's a very common accident that is easy to miss.
We took g(x) - f(x)
And you did plug the function in the right places, but note that it is subtracting the entire part of f(x).
3x - 9 - (5x - 1)
Not just 5x. Do you follow how that is different from 3x - 9 - 5x - 1?

Answer 5

Why are the x terms repeated in the answers rather than consolidated?

Answer 6

No I don't understand

Answer 7

what am I suppose to subtract?

Answer 8

I think it was meant to be 3^x, although it was not clear in the original problem. Fortunately it does not hinder the process either way!

I like to enclose things I substitute in brackets so that it is clear that the entire item is being acted on.
In our case we are plugging in f(x) and g(x). So doing so in:
g(x) - f(x)
(3^x - 9) - (5x - 1)
The parentheses don't matter for the first case. But then we are subtracting off the entire (5x - 1) part. It is equal to subtracting each individual part.
3^x - 9 - 5x - (-1)

Answer 9

An easier example to see... We subtract 3+2 from 5.
5 - (3 + 2)
Order of operations means to do parentheses first.
5 - (5)
5 - 5
0 So if we approach this any way, we have to get 0.

If we just put the minus sign on the first term like you were doing originally with the f(x):
5 - 3 + 2 = 2 + 2 = 4. That's not right! We only subtracted part of the whole thing!
But if we pull that negative sign through to all terms, we get what we wanted:
5 - 3 - 2 = 2 - 2 = 0. There we go!

Answer 10

I'm still getting the wrong answer

Answer 11

You want the quantity g(x) - f(x). Why not set up this subtraction as follows:

g(x) = 3x - 9
-f(x) =-(5x-1)
----- -------

Hint: 3x - 5x = ??
Hint: -9 - (-1) = ??

Answer 12

And so, g(x) - f(x) = ??

Answer 13

it's not that type of 3x. It's like this 3^x. The exponent x.