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Question 894434: Let f(t)=2-3t^2. Find
(A) f(-2) (B) f(-t)
(C) -f(t) (D) -f(-t)
Answer by alakazam2192(3)   (Show Source):
You can put this solution on YOUR website! 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!
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