First slide

Functions (XII)

Question

The period of the function $f (x) = \sqrt{\tan x} is$

Moderate

A

$π$
B

2 $π$
C

$\frac{π}{2}$
D

None of these

Solution

Let f(T + x) = f (x)
$\begin{array}{l} \Rightarrow \sqrt{\tan (T + x)} = \sqrt{\tan x} \Rightarrow \tan (T + x) = \tan x \\ \Rightarrow T + x = nπ + x, n \in Z \end{array}$
Clearly, from here, the least positive value of T independent of x is $π$ . Therefore, f (x) is a periodic function of period $π$ .

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