Thanks!!
Looking for a quick way to find f^-1(#) if asked to do so.
remember, if $\displaystyle f(x) = \#$ then $\displaystyle f^{-1}(\#) = x$
so when they ask for, say, $\displaystyle f^{-1}(2)$, they are looking for the $\displaystyle x$ value such that $\displaystyle f(x) = 2$
so find a point on the graph where $\displaystyle y = 2$ and the corresponding $\displaystyle x$ value is $\displaystyle f^{-1}(2)$
yes, $\displaystyle y = f(x)$, right?
so they ask you to find $\displaystyle f^{-1}(2)$, you don't know what it is, so equate it to a variable. this variable can be anything, but i chose $\displaystyle x$ because the answer will be an $\displaystyle x$-value
So let $\displaystyle f^{-1}(2) = x$
$\displaystyle \Rightarrow f \left(f^{-1}(2) \right) = f(x)$
$\displaystyle \Rightarrow 2 = f(x)$
So now we need to know what $\displaystyle x$ has to be so that $\displaystyle f(x)$, that is, the correspoding y-value for $\displaystyle x$, is 2