Let f(x) = ( ( | x | + 2 [ x ] ) ) where [.] represents greatest … - Vidyadip

MCQ

Let $f(x)$ = $\cos \left( {\pi \left( {\left| x \right| + 2\left[ x \right]} \right)} \right)$ 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 $[-1,1]$
✓
$f(x)$ = $|f(x)|$ for all $x$ .

✓

Answer

Correct option: D.

$f(x)$ = $|f(x)|$ for all $x$ .

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

$f(-x)=f(x)$ hence function is even.

It is a periodic function

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

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