First slide

Functions (XII)

Question

The period of the function f (x) = cos x² is

Moderate

A

2 $π$
B

$π$
C

$\frac{π}{2}$
D

None of these

Solution

Let f (T + x) = f (x) ⇒ cos (T + x)² = cos x²
⇒ (T + x)² = 2n $π$ ± x²
Clearly, from here, no positive value of T independent of x is possible because x² on R.H.S. can be cancelled only when T = 0.
$∴$ f (x) is a non periodic function.

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