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JEE Main 202125 JulyEvening Shift

Exam: JEE Main
Year: 2021
Date: 25 July
Shift: Evening Shift
Subject: Mathematics
Chapter: Functions

JEE Main 2021 · 25 July · Evening Shift · Mathematics · Functions

Consider function f: A → B and g: B → C(A, B, C ⊆ R) such that...

Consider function

f: A \to B and

g: B \to

C\left(A, B, C ⊆ R\right)

such that

{\left(gof\right)}^{- 1}

exists, then:

Options

A $f$ and $g$ both are one-one
B $f$ and $g$ both are onto
C $f$ is one-one and $g$ is onto
D $f$ is onto and $g$ is one-one

Correct answer

C. $f$ is one-one and $g$ is onto

Step-by-step solution

$∴ {\left(gof\right)}^{- 1}$ exist $⇒$ $gof = g\left(f\left(x\right)\right)$ is bijective

$⇒ f$ must be one-one and $g$ must be onto.

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