If $f:\left[0,\frac{π}{2}\right] → [0,∞)$ be a function defined by $y=\sin(\frac{x}{2})$, then f is
Answer & explanation
Correct answer: option 1
$y=\sin\frac{x}{2}$
$0≤x≤\frac{π}{2}⇒0≤\frac{x}{2}≤\frac{π}{4}⇒0≤\sin\frac{x}{2}≤\frac{1}{\sqrt{2}}$
$\left(0,\frac{1}{\sqrt{2}}\right)⊂[0,∞)$
So function is not surjective but function is injective as for any $0≤x≤\frac{π}{2},\sin\frac{x}{2}$ gives unique image.