Question

what is (f - g)(x)?

f(x) = -3x² + 9x

g(x) = 2x²

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 \(f(x)=-3x^{2}+9x\) and \(g(x) = 2x^{2}\), so substitute these into the formula:
\((f - g)(x)=(-3x^{2}+9x)-2x^{2}\)

Step3: Combine like terms

Combine the \(x^{2}\) terms: \(-3x^{2}-2x^{2}=-5x^{2}\), and the \(9x\) term remains as it is. So we get \((f - g)(x)=-5x^{2}+9x\)

Answer:

\(-5x^{2}+9x\)