Let be an even function satisfying for all and f(x)= cases 3x,&0 x<1, 4-x,&1 x 4

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)

for all

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