If g(y) = (y)^[y] where [.] denotes smallest integer function then find the value of g(- 3/2)?

Question

Question

Answer 1

Concept:

Smallest integer function (Ceiling function):

It is a function that takes all the values (−∞,∞) and gives only the integer

part i.e. range of the smallest integer the function is Z (all integers).

For e.g., [5.1] = 6, [- 5.1] = - 5

Calculation:

Given: g(y) = (y)[y] where [.] denotes the smallest integer function

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

⇒ g(- 3/2) = (-3/2)^{[- 3/2]}

As we know that, [- 3/2] = [-1.5] = - 1

⇒ g(- 3/2) = (- 3/2)^-1 = - 2/3

Confusion Points

Greatest integer function (Floor Function):

The greatest integer function is a function that gives the greatest integer

less than or equal to a given number. The greatest integer less than or

equal to a number x is represented as ⌊x⌋.

For e.g [5.1] = 5 & [- 5.1] = - 6