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

R

and

R

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[0, π]

and

[0, 1]

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[0, \frac{π}{2}]

and

[- 1, 1]

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[\frac{- π}{2}, \frac{π}{2}]

and

[- 1, 1]

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Solution

The correct option is C $[0, \frac{π}{2}]$ and $[- 1, 1]$
Since, $f : X \to Y$ , then $f (x) = sin x$

Now, take option C.

Domain $= [0, \frac{π}{2}]$ , Range $= [- 1, 1]$

For every value of $x$ , we get unique value of $y$ . But the value of

Thus function is one-one but not onto.

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