Question

what is $(f - g)(x)$?
$f(x) = -5x$
$g(x) = -3x^2 - 6x$
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 \(f(x)=-5x\) and \(g(x) = - 3x^{2}-6x\), so substitute these into the formula:
\((f - g)(x)=-5x-(-3x^{2}-6x)\)

Step3: Distribute the negative sign

Using the distributive property \(a-(b + c)=a - b - c\), we get:
\((f - g)(x)=-5x + 3x^{2}+6x\)

Step4: Combine like terms

Combine the \(x\)-terms: \(-5x+6x=x\), so the expression becomes:
\((f - g)(x)=3x^{2}+x\)

Answer:

\(3x^{2}+x\)