Question

If $f\left(x\right)$ is a periodic function of the period $k$ then$f(kx+a),$ where $a$ is a constant, is a periodic function of the period

• A. $k$
• B. $1$
• C. $\frac{k}{a}$
• D. none of these

Answer 1

Answer: (B)

$1$

Let $f\left(x\right)=\sin \left(x\right)$

Hence $k=2\pi$

Therefore $f(kx+a)$
$=\sin (2\pi x+a)$
$=\sin \left(a\right)$

$=$ constant

Hence period will be $1$.