If f(x) = e^x and g(x) = ⌈x) where ⌈.) denotes smallest integer function then find the value of f o g(9/2) ?

Concept:

Smallest integer function:(Ceiling function)

The function f (x) = [x) is called the smallest integer function and it means that the smallest integer greater than or equal to x i.e [x) ≥ x.

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) = ex and g(x) = ⌈x) where ⌈.⌉ denotes smallest integer function

Here, we have to find the value of f o g(9/2)

⇒ f o g(9/2) = f(g(9/2))

Since, g(x) = [x)

⇒ g(9/2) = [4.5) = 5

⇒ f o g(9/2) = f(5)

Since, f(x) = e^x 

⇒ f(5) = e⁵

Hence, f o g(9/2) = e⁵.