Consider function f : A → B and g : B → C A , B , C ⊆ R such that g o f - 1 exists, then:

∴ g o f - 1 exist ⇒ g o f = g f x is bijective ⇒ f must be one-one and g must be onto.

Mathematics - Functions Question with Solution | TestHub

MathematicsFunctionsTypes of Function (Mapping)Easy2 minPYQ_2021

MathematicsEasysingle choice

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

Answer:

Solution:

$∴ {(g o f)}^{- 1}$ exist $\Rightarrow$ $g o f = g (f (x))$ is bijective

$\Rightarrow f$ must be one-one and $g$ must be onto.

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Types of Function (Mapping)

⏱ 2mℹ️ Source: PYQ_2021

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