Functions: Consider functions f:Ato B and g:Bto C ( A,B,CsubseteqmathbfR ) such… | JEE Main 2021

JEE Main 2021 (Online) 25th July Evening ShiftQuestion 1

Consider functions $f:A\to B$ and $g:B\to C$ ($A,B,C\subseteq\mathbf{R}$) such that $(g\circ f)^{-1}$ exists, then :

Functions

$f$ is one-one and $g$ is onto✓ Correct answer$f$ and $g$ both are one-one$f$ is onto and $g$ is one-one$f$ and $g$ both are onto

Solution

$(g\circ f)^{-1}$ exists iff $g\circ f$ is bijective. Then $f$ must be one-one and $g$ must be onto.

Functions - JEE Mathematics question (JEE Main 2021 (Online) 25th July Evening Shift)