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\lfloor\frac{6x^2+13}{x^2+2}\right\rfloor\right),\quad \forall x\in\mathbb{R},

and

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

Here,

\lfloor y\rfloor

denotes the greatest integer less than or equal to

y

. The area bounded by the graph of

f(x)

and the

x

-axis from

x=-1

x=9

is (a)

\frac{31}{2}

(b) 15 (c) 12 (d)

\frac{15}{2}