To solve the problem of finding [tex]\( f(8.6) \)[/tex] for the function [tex]\( f(x) = \lceil x \rceil - 5 \)[/tex], follow these steps:
1. Identify the given function and value:
- The function is [tex]\( f(x) = \lceil x \rceil - 5 \)[/tex].
- We need to evaluate this function at [tex]\( x = 8.6 \)[/tex].
2. Apply the ceiling function:
- The ceiling function [tex]\(\lceil x \rceil\)[/tex] is defined as the smallest integer greater than or equal to [tex]\( x \)[/tex].
- For [tex]\( x = 8.6 \)[/tex], we find that [tex]\(\lceil 8.6 \rceil = 9\)[/tex].
3. Substitute the ceiling value into the function:
- Now, substitute the ceiling value into the function.
- So, [tex]\( f(8.6) = 9 - 5 \)[/tex].
4. Perform the arithmetic operation:
- Subtract 5 from 9 to find the result.
- Therefore, [tex]\( 9 - 5 = 4 \)[/tex].
So, [tex]\( f(8.6) = 4 \)[/tex].
Hence, the correct answer is [tex]\(\boxed{4}\)[/tex].
