I know what a Greatest Integer Function is but I do not under stand how to solve problems based on it. For example, how do I solve the following?

-1<=[2x^2-3]<=1

[2x^2-3] = [2x]

greatest integer function means largest integer less than or equal to it.

given that -1<=[2x]=<1

so 2x is a negative decimal less than -1 or zero or a positive integer less than 1

case 1 negative decimal less than zero

let it be [-0.4] = 0

case 2 zero

[0] = 0

case 3

let it be [0.2] = 0

so the answer is zero in every case