Let be an even function satisfying f(x-2)=f (x+ [ 6x^2+13 x^2+2 ] )

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

Let

f

be an even function satisfying

f(x-2)=f\left(x+\left[\frac{6x^2+13}{x^2+2}\right]\right),\qquad \forall x\in\mathbb{R},

and

f(x)=\begin{cases}3x,&0\leq x<1,\\4-x,&1\leq x\leq4.\end{cases}

Here

[y]

denotes the greatest integer function. The value of

f(-89)-f(67)+f(46)

is (a) 4 (b) 5 (c) 6 (d) 7