precalculus help: relations and functions..!?

Question

please help me out here! heres the problem:

[x] is the greatest integer not greater than x.
if f(x)= [2x]-3x, find the value of f(0).

thats just one. there are others, such as f(0.5), f(-3.5), etc.

THANK YOU IN ADVANCE!

Answer 1

f(x) = [2x] - 3x is the same as f(x) = -x

so, f(0) = 0, f(.5) = -0.5, f(-3.5) = 3.5

Answer 2

If [x] is the greatest integer not greater than x (floor function, basically), then for 0, it would still be 0.
So, 2(0) - 3(0) would indeed be 0.
However for f(0.5), the greatest integer would be 0. So, your function becomes 2(0) - 3(0.5), which gives -1.5.
For f(-3.5), the greatest integer would be -4. So, your function
becomes 2(-4) - 3(-3.5).
The rest of the values should be calculated similarly.

Answer 3

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

f(.5) = [2*.5] - 3*.5 = [1] - 1.5 = 1 - 1.5 = -.5

f(-3.5) = [2*-3.5] - 3*-3.5 = [-7] + 10.5 = -7 + 10.5 = 3.5

Answer 4

You just plug in the number in parenthesis into the given problem, f(-3.5)= [2(-3.5)]-3(3.5)

f(-3.5)= 7- 10.5
f(-3.5)=-3.5