Let f : R → R : f(x) =x^{2} and g : C → C: g(x) =x^{2}, where C is the set of all complex numbers. Show that f ≠ g.

It is given that f : R → R and g : C → C

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

We know that, Real numbers ≠ Complex Number

∵, Domain (f) ≠ Domain (g)

∴ f(x) and g(x) are not equal functions

∴ f ≠ g

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