Question

what is $(f + g)(x)$?
$f(x) = -x + 1$
$g(x) = -x^2$
write your answer as a polynomial or a rational function in simplest form.

Explanation:

Step1: Recall the definition of function addition

The sum of two functions \((f + g)(x)\) is defined as \(f(x)+g(x)\).

Step2: Substitute the given functions

We know that \(f(x)=-x + 1\) and \(g(x)=-x^{2}\). So, we substitute these into the formula for \((f + g)(x)\):
\((f + g)(x)=f(x)+g(x)=(-x + 1)+(-x^{2})\)

Step3: Simplify the expression

We can rewrite the expression by combining like terms (but in this case, there are no like terms to combine, just re - order the terms):
\((f + g)(x)=-x^{2}-x + 1\)

Answer:

\(-x^{2}-x + 1\)