Question

For each of the following functions determine (f(x+h)-f(x)) / h and express your answer in simple form.

a) f(x)= 1/(x-4)

Answer 1

This is differentiation so if you know the rules for that you can get the answer quickly. But here I suppose you need to do the long algebra

Answer 2

it is not first principles as it is not taking the limit of h->0

Answer 3

f(x+h)=1/(x+h-4)
f(x) is given, so just use these and try to simplify the result as much as possible