For equality of functions $f$ and $g \ldots . . .$. (i) domain of $f=\operatorname{domain}$ of $g$ (ii)…
For equality of functions $f$ and $g \ldots . . .$.
(i) domain of $f=\operatorname{domain}$ of $g$
(ii) $f(x)=g(x)$
(iii) $x \in \operatorname{domain}$ of $f$
Both (i) and (ii) necessary
Both (ii) and (iii) are necessary
Both (i) and (iii) are necessary
All of the above
Solution
For equality of functions $f$ and $g$ it is necessary that
(i) domains of $f=\operatorname{domain}$ of $g$
(ii) $f(x)=g(x)$
and (iii) $x \in \operatorname{domain}$ of $f$.
So, all are necessary.