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

Do not know what to do for the following:

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

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

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

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

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

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

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

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

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

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

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