Consider function f : A → B and

Question:

Consider function $f: \mathrm{A} \rightarrow \mathrm{B}$ and

$\mathrm{g}: \mathrm{B} \rightarrow \mathrm{C}(\mathrm{A}, \mathrm{B}, \mathrm{C} \subseteq \mathbf{R})$ such that (gof) $^{-1}$ exists, then:

  1. $\mathrm{f}$ and $\mathrm{g}$ both are one-one

  2. $f$ and $g$ both are onto

  3. $\mathrm{f}$ is one-one and $\mathrm{g}$ is onto

  4. $\mathrm{f}$ is onto and $\mathrm{g}$ is one-one

Correct Option: , 3

Solution:

$\therefore$ (gof) $^{-1}$ exist $\Rightarrow$ gof is bijective

$\Rightarrow ' f$ ' must be one-one and ' $g$ ' must be ONTO

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