Show that the function
Question:

Show that the function $f: R \rightarrow R: f(x)=\sin x$ is neither one – one nor onto.

Solution:

$f(x)=\sin x$

$y=\sin x$

Here in this range, the lines cut the curve in 2 equal valued points of $y$, therefore, the function $f(x)=$ sin $x$ is not one – one.

Range of $f(x)=[-1,1] \neq R$ (codomain)

$\therefore f(x)$ is not onto.

Hence, showed that the function $f: R \rightarrow R: f(x)=\sin x$ is neither one – one nor onto.