Given (f+g)(x)=10-3x and (f-g)(x)=5x-14) find f(x) and g(x).

Question

So I was told to do:
(f+g)(f-g)=2f

2f=(10-3x)+(5x-14)=2x-4
f(x)=x-2

For g(x) I tried:

-2g=(10-3x)+(5x-14)=2x-4
g(x)=-x+2

is that correct?

Answer 1

Nope. You didn't do what I told you.

(f+g)-(f-g) = 2g
so,
2g = (10-3x)-(5x-14)
2g = 24-8x
g = 12-4x

Now just check to be sure that your answers work:

f+g = (x-2)+(12-4x) = 10-3x
now check f-g the same way