Question

what is $(f - g)(x)$?
$f(x) = 3x^2 + 4x$
$g(x) = -x^2$
write your answer as a polynomial or a rational function in simplest form.

Explanation:

Step1: Recall the definition of function subtraction

To find \((f - g)(x)\), we use the formula \((f - g)(x)=f(x)-g(x)\).

Step2: Substitute the given functions

We know that \(f(x) = 3x^{2}+4x\) and \(g(x)=-x^{2}\). So we substitute these into the formula:
\((f - g)(x)=(3x^{2}+4x)-(-x^{2})\)

Step3: Simplify the expression

When we subtract a negative, it is equivalent to adding the positive. So we have:
\((f - g)(x)=3x^{2}+4x + x^{2}\)
Then we combine like terms. The like terms for \(x^{2}\) are \(3x^{2}\) and \(x^{2}\). Combining them gives \(3x^{2}+x^{2}=4x^{2}\). The term \(4x\) has no like terms to combine with, so it remains as is. So the simplified form is \(4x^{2}+4x\).

Answer:

\(4x^{2}+4x\)