The set of all points where is increasing is

MATHEMATICS · Numerical · AoPS · Mathematics · Functions · Functions

Problem

The set of all points where

f(x)

is increasing is

(a,b)\cup(c,\infty)

. Find

[a+b+c]

, where

[\cdot]

denotes the greatest integer function, given that

f(x)=2f\left(\frac{x^2}{2}\right)+f(6-x^2),\quad \forall x\in\mathbb{R}

and

f''(x)>0

for all

x\in\mathbb{R}