Answer
(a.) $f(a+2)=3a^2+14a+15$.
(b.) $f(a+h)-f(a)=6ah+3h^2+2h$.
Work Step by Step
The given function is
$f(x)=3x^2+2x-1$
(a.) Plug $x=a+2$ into the given function.
$f(a+2)=3(a+2)^2+2(a+2)-1$
Clear the parentheses.
$f(a+2)=3a^2+12a+12+2a+4-1$
Simplify.
$f(a+2)=3a^2+14a+15$.
(b.) Plug $x=a+h$ into the given function.
$f(a+h)=3(a+h)^2+2(a+h)-1$
Clear the parentheses.
$f(a+h)=3a^2+6ah+3h^2+2a+2h-1$... (1)
Now plug $x=a$ into the given function.
$f(a)=3(a)^2+2(a)-1$
Clear the parentheses.
$f(a)=3a^2+2a-1$ ...(2)
Subtract function (2) from function (1).
$f(a+h)-f(a)=(3a^2+6ah+3h^2+2a+2h-1)-(3a^2+2a-1)$
Clear the parentheses.
$f(a+h)-f(a)=3a^2+6ah+3h^2+2a+2h-1-3a^2-2a+1$
Simplify.
$f(a+h)-f(a)=6ah+3h^2+2h$.
