Question

Perform the indicated operation

let f(x)=x^2-7x-9 find(a+h)-f(a) and simplify

Answer 1

f(x+h) = (x+h)^2 - 7 (x+h) - 9
so
f(x+h)=x^2 + 2 x h + h^2 -7x - 7 h - 9
f(x) = x^2 - 7x - 9
----------------------- subtract
f(x+h) - f(x) = 2 x h + h^2 - 7 h

that is all you asked
if you then want the derivative, divide by h, let h go to zero and look at the limit

(2 x + h - 7)
as h ---> 0 is
2x-7