If $f (t) = |t - 2|$, find $f (-t)$

Question

Why question:

If $f (t) = |t − 2|$, find $f (−t)$

has result: $|t + 2|$?

I don't understand it.

Answer 1

The notation $f(-t)$ says to take the expression for $f(t)$ and change all $t$ to $-t$. You get $$ f(-t) = |(-t)-2| = |-t-2| = |-(t+2)| = |t+2|. $$

Answer 2

$$f(-t)=|(-t)-2|=|(-1)(t+2)|=|-1||t+2|=|t+2|$$

Answer 3

$f(-t) = |-t - 2| = |-1||t + 2| = |t + 2|$.

Another way to describe the answer is:

$t + 2$ if $t \geq -2$ and $-t - 2$ if $t < -2$

because, when these two separate answers are combined, it gives the definition of $|t + 2|$.