Which point in the parabola x^2 is nearest to (1,0)? [Hint: Minimize the square of the distance-- this avoids square roots.]​

First thing to know is “(f+g)(x)” really means “f(x) + g(x)”.

In your situation,
f(x) + g(x) = (x/2 - 2) + (2x^2 + x -3)

Now, those parentheses are only there to show you where f(x) and g(x) went/came from.

But to finish simplifying that, you just need to combine like terms.

x + x/2 really means 1x + 1/2 x and that’s 3/2 x.
-2+(-3) = -5

So, you end up with 2x^2 + 3/2 x -5