Algebra of Functions

Question

Find and simplify the following for the function. (Assume h ≠ 0.)

f(x)=9x

f(a+h)-f(a)/h= ?

Answer 1

f(x) = 9sqrx

f(a) = 9sqra

f(a+h) =9sqr(a+h)

(f(a+h) - f(a))/h= (9sqr(a+h) - 9sqra)/h

= (9/h)(sqr(a+h) -sqra)