Question
Show that the function $f: R \to R$, defined as $f(x) = x^2$ , is neither one-one nor onto.
✓
Answer
We observe that 1 and $-1 \in R$ such that $f (-1) = f (1)$ i.e. there are two distinct elements in $R$ which have the same image. So, $f$ is not one-one.
Since $f (x)$ assumes only non-negative values. So, no negative real number in $R$ (co-domain) has its pre-image in domain of f i.e. $R$. Consequently $f$ is not onto.
These facts are evident from the graph of $f (x)$ as shown in Fig.
Since $f (x)$ assumes only non-negative values. So, no negative real number in $R$ (co-domain) has its pre-image in domain of f i.e. $R$. Consequently $f$ is not onto.
These facts are evident from the graph of $f (x)$ as shown in Fig.
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