First slide

Functions (XII)

Question

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

Moderate

A

$π$
B

2 $π$
C

$\frac{π}{2}$
D

None of these

Solution

$\begin{array}{l} Let f (T + x) = f (x) \Rightarrow \sin \sqrt{T + x} = \sin \sqrt{x} \\ \Rightarrow \sqrt{T + x} = nπ + (- 1)^{n} \sqrt{x} \end{array}$
Clearly, from here, no positive value of T independent of x is possible because $\sqrt{x}$ on RHS can be cancelled only when T = 0.
$∴$ f (x) is a non-periodic function.

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