Answer
(a.) $ f(x_1+x_2)=mx_1+mx_2+b $.
(b.) $ f(x_1)+f(x_2) = mx_1+mx_2+2b $.
(c.) Not true
Work Step by Step
The given linear function is
$ f(x)=mx+b $
(a.) For $ f(x_1+x_2) $ plug $ x=x_1+x_2 $ into the given function.
$ f(x_1+x_2)=m(x_1+x_2)+b $
$ f(x_1+x_2)=mx_1+mx_2+b $
(b.) For $ f(x_1)+f(x_2) $ plug $ x=x_1 $ and $x=x_2 $ into the given function.
$ f(x_1)=mx_1+b $
and $ f(x_2)=mx_2+b $
Add both equations.
$ f(x_1)+f(x_2) = mx_1+b+mx_2+b $
$ f(x_1)+f(x_2) = mx_1+mx_2+2b $
(c.)
From part (a.) and part (b.).
$ f(x_1+x_2)\neq f(x_1)+f(x_2) $
