If \( A=\left\{x:x\in R,-\displaystyle\frac{\pi}{2}\le x\le\displaystyle\frac{\pi}{2}\right\} \) and \( B=\{y:y\in R\ ,-1\ \le y\le\ 1\} \) and function \( f:A\to B \) defined by \( f(x)=\sin x \) , then \( f \) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → One-one and onto
One-one: sin x is strictly increasing on \( \left[-\frac{\pi}{2},\frac{\pi}{2}\right] \), so different values of x give different values of sin x.
Onto: as x runs over this interval, sin x takes every value from −1 to 1, which is the whole of B.
Hence f is one-one and onto.