Question

The function $f:X\to Y$ defined by $f(x)=Sinx$ is one-one but not onto if $X$ and $Y$ are respectively equal to,

• A. $[\frac{-\pi }{2}\frac{\pi }{2}]$ and $[-1,1]$
• B. $[0,\frac{\pi }{2}]$ and $[-1,1]$
• C. $[0,\pi ]$ and $[0,1]$
• D. $IR$ and $IR$

Answer 1

Answer: (B)

Since $f:X\to Y$, then $f(x)=\sin x$
Now, take option (c).
Domain = $\left[0,\frac{\pi }{2}\right]$, Range = [ - 1, 1]
For every value of x, we get unique value ol
y. But the value of y in [-1, 0) does not haw
any pre-image.
$\therefore$ Function is one-one but not onto.