Question

Let f(x)=-x+2 and g(x)=-3x-4. Find (g-f)(x).

Answer 1

The notation is a little sketchy, but I think you mean f(x)*g(x), right?

We'll use the substitution property of equality. This states that for any x and y, if x = y, then we can use y in place of x, or x in place of y as needed.
Since f(x) = 2x + 5, we can replace f(x) with 2x + 5. We can also replace g(x) with 3x - 4.

To find f(x) * g(x), make the necessary replacements:
f(x) * g(x)
=(2x + 5)*(3x-4). Now FOIL it out:
=6x2 -8x + 15x - 20
=6x2 + 7x - 20. Right

Answer 2

(g-f)(x) = g(x) - f(x) = (-3x-4) - (-x+2)
(-3x-4) - (-x+2)
-3x-4 - (-x+2)
Distribute the negative to -x and +2
-3x-4 - (-x+2)
-3x+4 + x - 2
Combine like terms
-3x +x -2 + 4
-2x + 2
(g-f)(x) = -2x + 2