+0

# One of my friend's questions from high school. LOL

+10
87
3
+1132

If $$f(x) = \begin{cases} 2x-5 &\quad \text{if } x \ge 3, \\ -x + 5 &\quad \text{if } x < 3, \end{cases}$$

then for how many values of x is $$f(f(x)) = 3$$?

Jul 12, 2022

#1
0

I graphed it!  There are 5 solutions.  LOL

Jul 12, 2022
#2
+1132
+7

unfortunately that's wrong.

nerdiest  Jul 12, 2022
#3
+251
+1

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 :)

Jul 12, 2022