If f(x) = 2^|x| and g(x) = [x] where [.] denotes greatest integer function then find the value of f o g (- 17/2) ?

Concept:

Greatest Integer Function: (Floor function)

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

Domain of [x] is R and range is I.

If f :A → B and g : C → D. Then (fog) (x) will exist if and only if co-domain of g = domain of f i.e D = A and (gof) (x) will exist if and only if co-domain of f = domain of g i.e B = C.

Calculation:

Given: f(x) = 2^|x| and g(x) = [x] where [.] denotes greatest integer function 

Here, we have to find out the value of f o g (- 3/2)

⇒ f o g (- 17/2) = f( g(- 17/2))

∵ g(x) = [x], so g(- 17/2) = [- 17/2] = - 9

⇒ f o g(- 17/2) = f(- 9)

∵ f(x) = 2^|x| so, f(- 9) = 2^{|- 9|} = 2⁹ = 512

Hence, f o g (- 17/2) = 512