To find [tex]\( f(8.6) \)[/tex] for the function [tex]\( f(x) = \lceil x \rceil - 5 \)[/tex], follow these steps:
1. Identify the ceiling function: The ceiling function [tex]\( \lceil x \rceil \)[/tex] rounds [tex]\( x \)[/tex] up to the smallest integer that is greater than or equal to [tex]\( x \)[/tex].
2. Apply the ceiling function: For [tex]\( x = 8.6 \)[/tex], the ceiling [tex]\( \lceil 8.6 \rceil = 9 \)[/tex] because 9 is the smallest integer greater than 8.6.
3. Substitute the ceiling value into the function:
[tex]\[
f(8.6) = \lceil 8.6 \rceil - 5
\][/tex]
4. Calculate the resulting value:
[tex]\[
f(8.6) = 9 - 5 = 4
\][/tex]
Therefore, [tex]\( f(8.6) = 4 \)[/tex].
So, the answer is:
[tex]\[
\boxed{4}
\][/tex]
