First slide

Functions (XII)

Question

The period of the function $f (x) = \frac{| \sin x | - | \cos x |}{| \sin x + \cos x |} is$

Easy

A

$\frac{π}{2}$
B

2 $π$
C

$π$
D

None of these

Solution

We have,
$\begin{array}{l} f (π + x) = \frac{| \sin (π + x) | - | \cos (π + x) |}{| \sin (π + x) + \cos (π + x) |} \\ = \frac{| \sin x | - | \cos x |}{| \sin x + \cos x |} = f (x) for all x \end{array}$
$∴$ f (x) is periodic with period $π$ .

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