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Mark (√) against the correct answer in the following

Question:

Mark (√) against the correct answer in the following

$f:\left[\frac{-\pi}{2}, \frac{\pi}{2}\right] \rightarrow[-1,1]: f(x)=\sin x$ is

A. one - one and into

B. one - one and onto

C. many - one and into

D. many - one and onto

 

Solution:

$f:\left[\frac{-\pi}{2}, \frac{\pi}{2}\right] \rightarrow[-1,1]: f(x)=\sin x$

Here in this range, the function is NOT repeating its value,

Therefore it is one - one.

Range = Codomain

$\therefore$ Function is onto

Hence, option B is the correct choice.

 

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