Show that the function $f: R \rightarrow R$ defined as $f(x)=x^{2},$ is neither one-one nor onto.
Show that the function $f: R \rightarrow R$ defined as $f(x)=x^{2},$ is neither one-one nor onto.
since $f(-1)=1=f(1), \,f$ is not oneone. Also, the element $-2$ in the co-domain $R$ is not image of any element $x$ in the domain $R$ (Why ?). Therefore $f$ is not onto.
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