To solve the problem, let's follow the steps to find [tex]\( f(5.9) \)[/tex] for the given function [tex]\( f(x) = 3 \lfloor x - 2 \rfloor \)[/tex].
1. Identify the function definition:
The function is defined as [tex]\( f(x) = 3 \lfloor x - 2 \rfloor \)[/tex], where [tex]\( \lfloor \cdot \rfloor \)[/tex] denotes the floor function, which returns the greatest integer less than or equal to its argument.
2. Substitute the value [tex]\( x = 5.9 \)[/tex] into the function:
First, we need to calculate the expression inside the floor function:
[tex]\[ x - 2 = 5.9 - 2 \][/tex]
3. Carry out the subtraction:
[tex]\[ 5.9 - 2 = 3.9 \][/tex]
4. Apply the floor function:
The floor value of 3.9 is 3 because 3 is the greatest integer less than or equal to 3.9:
[tex]\[ \lfloor 3.9 \rfloor = 3 \][/tex]
5. Multiply by 3 as in the function definition:
[tex]\[ f(x) = 3 \times \lfloor x - 2 \rfloor = 3 \times 3 = 9 \][/tex]
Therefore, [tex]\( f(5.9) \)[/tex] is 9.
The correct answer is [tex]\( \boxed{9} \)[/tex].
