Question 894434
Any time we see a function f(x), f(t), etc., what's inside the parentheses is the variable used in the equation. For example, if our function is f(x), that means that x is the variable in its equation. Likewise, if we have f(1), replace any x value in the equation with 1. Therefore, to solve for part A, just replace t with -2:

f(-2) = 2 - 3(-2)^2
      = 2 - 3(4) 
      = -10

For part B, we will now replace t with -t, since that's what the function is telling us to do: 

f(-t) = 2 - 3(-t)^2
      = 2 - 3(t^2)
This is because -t * -t is t^2, positive.

Part C is a little bit different. First things first, the variable inside the parentheses of the function is t, so there's nothing we need to replace it with this time. However, there is a negative sign on the outside, which indicates we should make our whole function negative.

-f(t) = -(2 - 3(t)^2)
      = -2 + 3(t)^2

When we make an equation negative, every sign we had before, flips to the opposite sign: positive to negative, and negative to positive.

Lastly, part D combines the rules in B and C together:

-f(-t) = -(2 - 3(-t)^2)
       = -2 + 3(t^2)

Just as an FYI as well, f(-t) represents that the function is being reflected over the y-axis of a graph, and -f(t) represents that the function is being reflected over the x-axis of a graph. 

I hope this explanation helped!