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I am having a hard time with this math problem :(

g(x)=-x^2+9x
solve for g(a+h).

Just sub a+h in for x.

$g(a+h)=-(a+h)^{2}+9(a+h)$

I don't see anything to solve though.

Or are you trying to find the derivative of $-x^{2}+9x$ by using the definition of a derivative, but have it poorly worded?

The definition of a derivative is $g'(x)=\lim_{h\to 0}\frac{g(x+h)-g(x)}{h}$

Is that what you're getting at? Just a thought.

That's how far I got, now it's the "FOIL" and distributing stuff that I'm stuck on.

No... no derivatives involved here... It's more of a college algebra review.

I am not trying to be rude, but one learns FOIL in beginning algebra. You are in a calculus

class, so you may be in trouble. You had better see your instructor. The algebra is what

gives most students trouble in calculus. One should have algebra down pat before taking

calculus.

Upon subbing the a+h in for x, we can factor out an a+h

$-(a+h)(a+h-9)$ and expand

or just expand $-(a+h)^{2}+9(a+h)$

$= -(a+h)(a+h)+9(a+h)$

FOIL stands for First, Over, Inside, Last.

First would be $a\cdot a=a^{2} \;\ \text{Over}=a\cdot h, \;\ \text{Inside}=a\cdot h, \;\ \text{Last}=h^{2}$

Remember, the negative in the front. So, we have:

$=-a^{2}-2ah-h^{2}+9a+9h$