Question

what is $(f - g)(x)$?
$f(x) = -2x^2 - 7x$
$g(x) = 4x + 5$
write your answer as a polynomial or a rational function in simplest form.

Explanation:

Step1: Recall the definition of \((f - g)(x)\)

By the definition of function subtraction, \((f - g)(x)=f(x)-g(x)\).

Step2: Substitute the given functions

We know that \(f(x)=-2x^{2}-7x\) and \(g(x) = 4x + 5\), so substitute these into the formula:
\((f - g)(x)=(-2x^{2}-7x)-(4x + 5)\)

Step3: Distribute the negative sign

Distribute the negative sign to each term in \(g(x)\):
\((f - g)(x)=-2x^{2}-7x-4x - 5\)

Step4: Combine like terms

Combine the \(x\)-terms: \(-7x-4x=-11x\)
So, \((f - g)(x)=-2x^{2}-11x - 5\)

Answer:

\(-2x^{2}-11x - 5\)