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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