SOLUTION: if f(x) (function of x)=x^2+5, find function (a+h)- function (a)

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Question 45769: if f(x) (function of x)=x^2+5, find function (a+h)- function (a)
Answer by tutorcecilia(2152) About Me  (Show Source):
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f(a+h) = x^2+ 5 =(a+h)^2 + 5 [Plug the function into the original equation]
f(a) = x^2+5 = a^2 + 5 [Plug the function into the original equation]
So, f(a+h) - f(a) =
[(a+h)^2+5] - [a^2+5]
[(a+h)(a+h)+5] - [a^2+5]
[(a+h)(a+h)+5] - [a^2+5]
a^2 + 2ah + h^2 +5 - a^2 - 5 [Combine like-terms]
2ah + h^2 [Factor]
h(2a+h)[Final answer]