FunctionHard
Question
If ′f′ and ′g′ are bijective functions and gof is defined, then, gof must be:
Options
A.injective
B.surjective
C.bijective
D.into only
Solution
f(g(x1)) = f(g(x2))
⇒ g(x1) = g(x2)
as f is one - one function
⇒ x1 = x2
as g is one - one function
hence f(g(x1)) = f(g(x2))
⇒ x1 = x2
⇒ f(g(x)) is one - one function
⇒ g(x1) = g(x2)
as f is one - one function
⇒ x1 = x2
as g is one - one function
hence f(g(x1)) = f(g(x2))
⇒ x1 = x2
⇒ f(g(x)) is one - one function
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