How do I do a problem like this F(x+h)?
Okay, in this problem F(x)=2x+1, H(x)= -x^2+x-1. The problem is F(x+h)-F(x). I know that in functions, you are supposed to substitute the () for the x value in the respective function. But I'm not exacty sure what I'm supposed to do with F(x+h). I don't think my teacher instructed me and it's been a long summer 
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Comments
The value in the parenthesis of F(x) is represented by x. And everywhere you see an x in the function { 2x + 1 } you put whatever value is in those parentheses.
Soooooo . . .
If you have F(x) = 2x + 1,
and you want to know what F(x + h),
it will look like this:
F(x+h) = 2(x+h) + 1 = 2x + 2h + 1
And to get F(x+h) - F(x)
[ 2(x+h) + 1] - [2x + 1]
2x + 2h + 1 - 2x - 1
rearranging terms
(2x - 2x) + 2h + (1 - 1)
0 + 2h + 0
2h = F(x+h) - F(x)
F(x) is the value of the function when the variable receives the value x.
When the variable increases by h, its new value is x + h, and your teacher asked you to evaluate the corresponding value of the function.
If F(x) = 2x + 1,
then F(x+h) = 2(x + h) + 1
and the change in value of the function is
F(x+h) - F(x) = [2(x + h) -1] - [2x - 1] = 2h
If the value of the variable change an amount h, the corresponding change in value of the function is 2h in this case
you would substitute x in f(x) with (x+h):
F(x+h)-F(x)=
2(x+h)+1 - (2x+1)=
2x+2h+1-2x-1=
2x and 1 cancel out leaving you
2h
as your answer.
If you have to take it a step further and substitute h for H(x) then you would continue as so...
2(-x^2+x+1)
-2x^2+2x+2
F(x+h) means to replace all x's with x + h
F(x+h) = 2(x+h) + 1 = 2x + 2h + 1
so F(x+h) - F(x) = 2x + 2h + 1 - (2x + 1)
2x + 2h + 1 - 2x -1 = 2h <---- ANSWER
Good luck to you !
Okay, I'm changing my answer cuz I didn't read it very well and left part of it out...
f(x+h) = F(x) + f(h(x))
So, f(x+h)-f(x)= f(h(x))
and then you'll get the whole equation h(x) and plug it in for all the x's in the original f(x) equation with it and then you'll get your answer.
And please don't listen to anyone else. They're half-way right but they don't get that it wants you to use the addition rule for functions. My answer may not be right but I have the right idea.