Algebra 2 function help!

[zach223]

I did my best to solve this problem, but I have no idea how to do it.

A lower case L is the absolute value sign in the problem.

Given f(x)=6-2x-x^2, g(x)= l2x+1l, and h(x)=(x+3)/(x-5)
and then the problem is: g(x+h)

What I really don't understand for this is how do I figure out h?
I don't want you to do the problem for me, just explaining how to do it works, unless the only or best way to explain is to show.

 

[tkhunny]

Do you understand function notation? Substitute into the definition WHATEVER is in the argument.

If f(x) = 3x + 2, then

f(2) = 3(2) + 2
f(r) = 3r + 2
f(house) = 3(house) + 2
f(f(x)) = 3(f(x)) + 2 = 3(3x+2) + 2 = 9x + 4 + 2 = 9x + 6
f(f(x)+2) = 3(f(x)+2) + 2 = 3(f(x)) + 6 + 2 = 3(3x+2) + 8 = 9x + 6 + 8 = 9x + 14