Question

what is (f - g)(x)? Writer your answer as a polynomial.
f(x) = -2x^2 + 2x + 4
g(x) = -x + 5

Answer 1

To find \((f - g)(x)\), we need to subtract the function \(g(x)\) from the function \(f(x)\):

Given:
\[
f(x) = -2x^2 + 2x + 4
\]
\[
g(x) = -x + 5
\]

Now, we perform the subtraction:
\[
(f - g)(x) = f(x) - g(x)
\]

Substituting the expressions for \(f(x)\) and \(g(x)\):
\[
(f - g)(x) = (-2x^2 + 2x + 4) - (-x + 5)
\]

Distributing the negative sign in front of \(g(x)\):
\[
(f - g)(x) = -2x^2 + 2x + 4 + x - 5
\]

Now combine like terms:
\[
= -2x^2 + (2x + x) + (4 - 5)
\]
\[
= -2x^2 + 3x - 1
\]

Therefore, the polynomial \((f - g)(x)\) is:
\[
\boxed{-2x^2 + 3x - 1}
\]