If f(x) = [x] where [.] denotes the greatest integer function and g(x) = log2 x then find the value of g o f(5/2) ?

If f(x) = [x] where [.] denotes the greatest integer function and g(x) = log2 x then find the value of g o f(5/2) ? Correct Answer 1

Concept: 

Greatest Integer Function: (Floor function)

The function f (x) = is called the greatest integer function and means greatest integer less than or equal to x i.e ≤ x.

Domain of is R and range is I.

where denotes the greatest integer function and g(x) = log2 x

Here we have to find the value of g o f(5/2)

⇒ g o f(5/2) = g( f(5/2))

∵ f(x) = so, f(5/2) = = 2

⇒ g o f(5/2) = g(2)

∵ g(x) = log2 x so, g(2) = log₂ 2 = 1

Hence, g o f(5/2) = 1