If f(x)={2x−5if x≥3,−x+5if x<3,
then for how many values of x is f(f(x))=3?
I think it would be a good idea if you solve this for yourself. :)
Do some casework!
Set up some cases such as x >= 3, and where x < 3. Remember, just because x >= 3, doesn't mean that f(x) is also greater than or equal to 3, set up some cases there too! There may also be extraneous solutions! Get rid of those :)