If $f(x)=\lceil x\rceil-5$, what is $f(8.6)$?

Evaluate the ceiling function: ⌈ 8.6 ⌉ = 9 .
Substitute the result into the function: f ( 8.6 ) = 9 − 5 .
Perform the subtraction: 9 − 5 = 4 .
The final answer is: 4 ​ .

Explanation

Understanding the Problem We are given the function f ( x ) = ⌈ x ⌉ − 5 and we want to find f ( 8.6 ) . The ceiling function, denoted by ⌈ x ⌉ , returns the smallest integer greater than or equal to x .

Evaluating the Ceiling Function First, we need to evaluate the ceiling function at x = 8.6 . The smallest integer greater than or equal to 8.6 is 9 . Therefore, ⌈ 8.6 ⌉ = 9 .

Substituting into the Function Now, we substitute this value into the function f ( x ) = ⌈ x ⌉ − 5 . So, f ( 8.6 ) = ⌈ 8.6 ⌉ − 5 = 9 − 5 .

Calculating the Final Result Finally, we perform the subtraction: 9 − 5 = 4 . Therefore, f ( 8.6 ) = 4 .


Examples
Imagine you're at a store where prices are always rounded up to the nearest dollar. If an item costs $8.60, the store charges you $9.00. Now, if you have a $5 off coupon, the final price you pay is $9 - $5 = $4. This is exactly how the given function works: it rounds up to the nearest integer and then subtracts 5.

Answered by GinnyAnswer | 2025-07-08