State the type of function f: N N, f(x)=x^ 2 - Vidyadip

Question

State the type of function $f: \mathbf{N} \rightarrow \mathbf{N}, f(x)=x^{2}$

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Answer

Domain $\mathrm{D}_{f}=\mathrm{N}=\{1,2,3, \ldots\}$
Co-domain $\mathrm{B}=\mathrm{N}=\{1,2,3, \ldots\}$
$f(x)=x^{2} .$ By substituting the values of $x=1,2,3, \ldots$ the images are $1,4,9, \ldots$
Thus, for two different values of domain their images in co-domain are different. Hence, the given function is one - one function.

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