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


f(x) = sinx


y = sinx


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



Range of f(x) = [ - 1,1]≠R(codomain)


f(x) is not onto.


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


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