Question:
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.
Solution:
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
$\therefore \mathrm{f} \neq \mathrm{g}$