The symbol [x] means the greatest integer not greater than x. If f(x)=[2x]-3x, find the value for f(x-1).
Thanks.
f(x-1)= [2(x-1)]-3(x-1)
=2x-2-3x+3
=-x+1
So you just take away the brackets? Why are you able to do that?
To find the value of f(x-1), we need to substitute x-1 into the function f(x).
First, let's substitute x-1 into the function [2x]:
[2(x-1)]
Next, simplify the expression:
[2x - 2]
Now, let's substitute x-1 into the function 3x:
3(x-1)
Expand the expression:
3x - 3
Finally, let's subtract the value we obtained from [2x] from the value we obtained from 3x:
(3x - 3) - [2x - 2]
Distribute the negative sign:
3x - 3 - 2x + 2
Combine like terms:
(3x - 2x) + (2 - 3)
x - 1
Therefore, f(x-1) = x - 1.
To find the value of f(x-1), we need to substitute x-1 in place of x in the expression for f(x) and evaluate it.
Given that f(x) = [2x] - 3x, let's substitute x-1 for x:
f(x-1) = [2(x-1)] - 3(x-1)
Now, let's simplify the expression step by step:
First, distribute the 2 and 3:
f(x-1) = 2(x-1) - 3(x-1)
Next, simplify within the parentheses:
f(x-1) = 2x - 2 - 3x + 3
Combine like terms:
f(x-1) = -x + 1
Therefore, the value of f(x-1) is -x + 1.