Question

The function $f\left(x\right)$ is defined on the interval $[0,1]$. Find the domain of the function:

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

• A. $2K\pi \le x\le 2K\pi +\pi$ where $K\in I$
• B. $K\pi \le x\le K\pi +\pi$ where $K\in I$
• C. $2K\pi \le x\le 2K\pi +\frac{\pi }{2}$ where $K\in I$
• D. none of these

Answer 1

The correct option is A $2K\pi \le x\le 2K\pi +\pi$ where $K\in I$

Given $f\left(x\right)$ defined in interval $[0,1]$

$\therefore f\left(\sin x\right)$ will be defined if $\sin x\in [0,1]$

$i.e\sin x\ge 0\Rightarrow 0\le x\le \pi$ in one period. We know

$\sin x$ is periodic with period $2\pi$

Hence $x\in [2k\pi ,2k\pi +\pi ]$ where $k\in I$