Question

If the function $y=\sin \left(f\right(x\left)\right)$ is monotonic in an interval of $x[$where $f\left(x\right)$ is continuous$]$ and the difference between the maximum and minimum value of $f\left(x\right)$ is $k\pi ,$ then the value of $(k+1)$ is

Answer 1

As, $y=\sin \left(f\right(x\left)\right)$ is monotonic for
$f\left(x\right)\in [2n\pi -\frac{\pi }{2},2n\pi +\frac{\pi }{2}]$ or $[2n\pi +\frac{\pi }{2},2n\pi +\frac{3\pi }{2}]$
$\therefore$ difference between the maximum and minimum value of $f\left(x\right)$ is $\pi$
$\Rightarrow k=1$