Bdmo 2014 regionals(a tweaked version of question):
If $f$ is a strictly increasing function over the reals with $f(f(x))=x^2+2$, then $f(3)=?$
Obviously,$f(3)=f(1)^2+2$ but I can't see where we are going to use the 'strictly increasing' fact.I don't think there is a way to reverse-engineer such a function without heavy machinery.I have plugged in loads of values but they have yielded nothing.Some help will be appreciated.
EDIT: As others have noted, such a function is not possible with our current domain, but:
If the function is defined over the positive reals, does $f(3)$ have a definite value?