Subjective Type

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

Solution

one-one function is a function that comprises individuality that never maps discrete elements of its domain to the equivalent element of its codomain. We can say, every element of the codomain is the image of only one element of its domain.

We know that $$\sin(0)=0$$ and $$\sin(\pi)=0$$.

Thus, $$0$$ and $$\pi$$ have the same image.

So, f is many-one.


Into Function : Function f from set A to set B is Into function if at least set B has a element which is not connected with any of the element of set A.

Range $$(f)=[-1, 1]\subset R$$. Hence, f is into.

So, f is neither one-one nor onto.

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