Question

The period of the function $f\left(x\right)=p|\sin x|+p^2|\cos x|+g\left(p\right)$ is $\frac{\pi }{2}$ , if $p$ is

• A. $1$
• B. $2$
• C. $3$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $1$

As we know, Period of $|\sin x|+|\cos x|=\frac{\pi }{2}$
$f\left(x\right)=p|\sin x|+p^2|\cos x|+g\left(p\right)$
So, at $p=1,f\left(x\right)=|\sin x|+|\cos x|+g\left(1\right)$
as $g\left(1\right)$ is a constant, so that its not going to affect the period of function.
$\therefore$ period of $f\left(x\right)=|\sin x|+|\cos x|+g\left(1\right)is\frac{\pi }{2}$