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 $f$
  1. Both (i) and (ii) necessary
  2. Both (ii) and (iii) are necessary
  3. Both (i) and (iii) are necessary
  4. 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.

Asked in: AP EAMCET 2020 (22 Sep Shift 1)

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