Question

If f(x) = −x2 − 8x + 7 and g(x) = x − 1 , what does (g − f) (x) equal?

Answer 1

x^2 + 9x - 8

Explanation:

(g - f)(x) means g(x) minus f(x)

Since

f(x) = −x2 − 8x + 7 and g(x) = x − 1

then we subtract g(x)–f(x)

x – 1 - (-x^2- 8x +7)

When we take off the parenthesis the minus in front of the parenthesis has to be distributed to all three terms inside.

x - 1 + x^2 + 8x -

Combine like terms. The x and 8x can be added and the -1 and -7 can be combined.

9x + x^2-8

Rearrange because usually the highest exponent goes first, then regular x and plain number last (constant)

x^2 + 9x- 8