Question

what is (f - g)(x)?
f(x) = 3x² + 6x
g(x) = x² + x
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 \(f(x) = 3x^{2}+6x\) and \(g(x)=x^{2}+x\), so substitute these into the formula:
\((f - g)(x)=(3x^{2}+6x)-(x^{2}+x)\)

Step3: Distribute the negative sign

Distribute the negative sign to each term in \(g(x)\):
\((f - g)(x)=3x^{2}+6x - x^{2}-x\)

Step4: Combine like terms

Combine the \(x^{2}\) terms and the \(x\) terms:
For the \(x^{2}\) terms: \(3x^{2}-x^{2}=2x^{2}\)
For the \(x\) terms: \(6x - x = 5x\)
So, \((f - g)(x)=2x^{2}+5x\)

Answer:

\(2x^{2}+5x\)