Questions: If f(x) = ⌈x⌉ - 5, what is f(8.6)?

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

Solution

Solution Steps

Step 1: Understand the function $ f(x) $

The function is defined as $ f(x) = \lceil x \rceil - 5 $, where $ \lceil x \rceil $ represents the ceiling function. The ceiling function returns the smallest integer greater than or equal to $ x $.

Step 2: Apply the ceiling function to $ x = 8.6 $

For $ x = 8.6 $, the ceiling function $ \lceil 8.6 \rceil $ returns the smallest integer greater than or equal to 8.6, which is 9.

Step 3: Subtract 5 from the result

Now, substitute the result of the ceiling function into the original function: \[ f(8.6) = \lceil 8.6 \rceil - 5 = 9 - 5 = 4. \]

Final Answer

$\boxed{4}$

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