1. Calculus HELP!

Do not know what to do for the following:

Find and simplify

f(a+h) - f(a)

for each function

f(x) = 4 - x^2

f(x) = x^2 +1

Do you understand functional notation at all?

Given a function $\displaystyle f(x)\!:\;f(a+h)$ means "replace each $\displaystyle x$ with $\displaystyle a+h$."

Do not know what to do for the following:

Find and simplify $\displaystyle f(a+h) - f(a)$ for each function:

$\displaystyle (1)\;f(x) \,= \,4 - x^2$

$\displaystyle (2)\;f(x)\,=\, x^2 +1$

We are asked to find; .$\displaystyle f(a+h) - f(a)$

Try to "read" what is says:
. . (a) Find $\displaystyle f(a+h)$ . . . replace $\displaystyle x$ with $\displaystyle a+h$.
. . (b) Then find $\displaystyle f(a)$ . . . replace $\displaystyle x$ with $\displaystyle a$.
. . (c) Then subtract them: .$\displaystyle f(a+h) - f(a)$

$\displaystyle (1)\;f(x)\:=\:4 - x^2$

. . $\displaystyle (a)\;f(a+h) \;= \; 4 - (a+h)^2\;=\;4 - (a^2 + 2ah + h^2) \;=$ $\displaystyle \;4 - a^2 - 2ah - h^2$

. . $\displaystyle (b)\;f(a)\;=\;4 - a^2$

. . $\displaystyle (c)\;f(a+h) - f(a)\;=\;(4 - a^2 - 2ah - h^2) - (4 - a^2) \;=$ $\displaystyle 4 - a^2 - 2ah - h^2 - 4 + a^2$

Answer: .$\displaystyle \boxed{-2ah - h^2}$

You see? . . . It's just basic Algebra . . .