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

Question

I'm not sure how to go about this.

Answer 1

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

You can find g(x) in a similar way.

Answer 2

So, g-g=0

wouldn't that get me g(x)=0?

Answer 3

come on; this is Algebra I

(f+g)-(f-g) = 2g

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

Answer 4

or, now that you know f,

f+g-f = g
so,
g(x) = (10-3x)-(x-2) = 12-4x