Question

Which of the following functions is non periodic

• A. $f(x) = x - \lbrack x\rbrack$
• B. $f(x) = \left\{ \begin{matrix} 1\text{ if x is a rational number} \\ \text{0 if x is an irrational number} \end{matrix} \right.\$
• C. $f(x) = \sqrt{\frac{8}{1 + \cos x} + \frac{8}{1 - \cos x}}$
• D. cos$\sqrt{x}$

Answer 1

Answer: (D)

cos$\sqrt{x}$

Answer 2

The function in (1) is periodic with period 1 and the function in (2) is also periodic since $f(x + r) = f(x)$for every rational $r.$ The function in (3) is equal to $\frac{4}{|\sin x|}$ and thus has period $\pi$.

All are periodic. In 'b' there is no period.