Question

Let $f\left(x\right)=cos\left(\pi \right(|x|+2\left[x\right]\left)\right)$ where [.] represents greatest integer function, then

• A. f(x) is neither odd nor even
• B. f(x) is non periodic function
• C. Range of f(x) is [-1,1]
• D. f(x) = |f(x)| for all x

Answer 1

The correct option is C Range of f(x) is [-1,1]

$f\left(x\right)=cos\left(2\pi \right[x]+\pi |x|)=cos\left(\pi |x|\right)$

$\Rightarrow f(-x)=-f\left(x\right)$ hence function is even. It is also periodic function.

From graph $f\left(x\right)=|f\left(x\right)|$ is not possible for all $x$.