Solve this


Let $f: R \rightarrow R: f(x)=x^{2}$ and $g: C \rightarrow C: g(x)=x^{2}$, where $C$ is the set of all

complex numbers. Show that f ≠ g.



It is given that $f: R \rightarrow R$ and $g: C \rightarrow C$

Thus, Domain $(f)=R$ and Domain $(g)=C$

We know that, Real numbers $\neq$ Complex Number

$\because$, Domain $(\mathrm{f}) \neq$ Domain $(\mathrm{g})$

$\therefore f(x)$ and $g(x)$ are not equal functions

$\therefore \mathrm{f} \neq \mathrm{g}$


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