JEE Advanced | 2015Set, Relation and FunctionHard
Question
Let ƒ(x) = 
for all for x ∈ 
and and g(x) = 
sin x for all x ∈ 
Let (ƒog)(x) denotes ƒ(g(x)) and (goƒ)(x) denotes g(ƒ(x)). Then which of the following is (are) true?
for all for x ∈ and and g(x) = sin x for all x ∈ Let (ƒog)(x) denotes ƒ(g(x)) and (goƒ)(x) denotes g(ƒ(x)). Then which of the following is (are) true?Options
A.Range of ƒ is 
B.Range of ƒ log is
C.
D.There is an x ∈ 
such that (goƒ)(x) = 1
such that (goƒ)(x) = 1Solution
(A) f(x) = sin 
, x ∈ R
= sin
= sin α, α ∈
(B) f(g(x)) = f(t), t ∈
⇒ f(t) ∈
(C)
= 1.
(D) g(f(x)) = 1 ⇒ sin f(x) =
but f(x) ∈
⇒ sin f(x) ∈
so no solutions
, x ∈ R= sin
= sin α, α ∈
(B) f(g(x)) = f(t), t ∈
⇒ f(t) ∈
(C)
= 1.
(D) g(f(x)) = 1 ⇒ sin f(x) =
but f(x) ∈
⇒ sin f(x) ∈
so no solutionsCreate a free account to view solution
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