Question

Let $f$ be an even function satisfying $f(x-2)=f\left(x+\left[\frac{6x^2+13}{x^2+2}\right]\right)\forall x\in R$ and $f(x)=\{\begin{array}{ll}3x,& 0\le x<1\\ 4-x,& 1\le x\le 4\end{array}$ Note : [.] denotes greatest integer function of $x)$ then the value of $f(-89)-f(-67)+f(46)$ is equal to

Answer 1

Answer: 4

Correct answer is (d)