Function Combination Math Problem... Help?

Question

First of all, if you don't know the answer please don't just post a response like "do your own homework, slacker!" Because this is a 180 question packet for school that I've already finished twice.

Both sets of my answers, my original packet, and all of my notes from the class last year then flew out of my car onto a Jimmy Buffet concert.

So I'm not a slacker, I just forget how to do a couple questions.

here's the question:

27. Simplify:

( f ( x + h ) - f ( x ) ) / h

where:

a. f ( x ) = 2 x + 3

b. f ( x ) = 1 / ( x + 1 )

c. f ( x ) = x ^ 2

there's a picture of this problem here:

http://s254.photobucket.com/albums/hh111/groupiegurl14334/?action=view&current=numba27.jpg

Answer 1

a)

f(x+h)-f(x)=2(x+h)+3 -(2x+3)=2h

=>[f(x+h)-f(x)]/h=2

b)

f(x+h)-f(x)=[1/(x+h+1)]-[1/(x+1)]

=((x+1)-(x+h+1))/(x+1)(x+h+1)

=(-h)/(x+1)(x+h+1)

=>[f(x+h)-f(x)]/h = -1/(x+1)(x+h+1)

c)

f(x+h)-f(x)=(x+h)^2-x^2=2xh+h^2

=>[f(x+h)-f(x)]/h=2x+h