Let f(x)= ( 6 ( 2 x ) ) for all x R and g(x)= 2 x for all x R . Let (f g)(x) denote f(g(x)) and (g f)(x) denote g(f(x)). Then which of the following is (are) true?

JEE Advanced 2015 Mathematics question

Let for all and for all . Let denote and denote . Then which of the following is (are) true?

Answer: (A),(B),(C)

(A) : true. (B) takes all values in , on which

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Question ID VK-026420