Answer
(a.)$f(a+2)=a^2+5$
(b.)$f(a+h)-f(a)=2ah+h^2-4h$.
Work Step by Step
The given function is
$f(x)=x^2-4x+9$
(a.) Plug $x=a+2$ into the given function.
$f(a+2)=(a+2)^2-4(a+2)+9$
Clear the parentheses.
$f(a+2)=a^2+4a+4-4a-8+9$
Simplify.
$f(a+2)=a^2+5$.
(b.) Plug $x=a+h$ into the given function.
$f(a+h)=(a+h)^2-4(a+h)+9$
Clear the parentheses.
$f(a+h)=a^2+2ah+h^2-4a-4h+9$
Simplify.
$f(a+h)=a^2+2ah+h^2-4a-4h+9$ ... (1)
Now plug $x=a$ into the given function.
$f(a)=(a)^2-4(a)+9$
Clear the parentheses.
$f(a)=a^2-4a+9$ ...(2)
Subtract function (2) from function (1).
$f(a+h)-f(a)=(a^2+2ah+h^2-4a-4h+9)-(a^2-4a+9)$
Clear the parentheses.
$f(a+h)-f(a)=a^2+2ah+h^2-4a-4h+9-a^2+4a-9$
Simplify.
$f(a+h)-f(a)=2ah+h^2-4h$.
