Part (a):

The brackets around the x indicate that it is a floor function (or a greatest integer function). This means we are looking for the greatest integer that is less than or equal to 0.

Remember that an integer is a whole number without any decimals or fractions and it can be either positive or negative. 0 is also an integer.

So, we are looking for the greatest integer less than or equal to 0. Because 0 is an integer, 0 is our answer.

Part (b):

The brackets around the x indicate that this is a ceiling function (or a least integer function). This means we are looking for the smallest integer greater than or equal to 0.

Again, because 0 is an integer, this is the smallest integer we can think of that is greater than or equal to 0.

Answer:

(a) 0 (b) 0