It is given that f(x) = x^3  3x + 1 .
Find the number of real roots of f(f(x))
Plotting the composite function
(x^3  3x + 1)^3  3(x^3  3x + 1) + 1
on a grapher, we see 7 real roots.
The flatness at x=1 is probably related to the loss of 2 real roots (gaining two imaginary or composite roots) as there doesn't seem to be a discontinuity there, though it is indeed not your typical maximum.

Posted by Charlie
on 20161129 13:59:19 