The symbol [x] means the greatest integer not greater than x. If f(x)=2[x]-3x find each value.?

Question

The symbol [x] means the greatest integer not greater than x. If f(x)=2[x]-3x find each value.


9. f(0)

10. f(.5)

I am so confused.

Answer 1

f(x) = 2[[x]] - 3x

The best way to describe the greatest integer function [[ ]] is to just truncate everything past the decimal point (for positive numbers).

9)

f(0) = 2[[0]] - 3(0)

The greatest integer not greater than 0 is 0, so

f(0) = 2(0) - 3(0) = 0

10.

f(0.5) = 2 [[ 0.5 ]] - 3(0.5)

The greatest integer not greater than 0.5 is 0, so we have

f(0.5) = 2(0) - 3(0.5)
= 0 - 1.5
= -1.5