To determine the value of [tex]\( f(5.9) \)[/tex] for the function [tex]\( f(x) = 3 \lfloor x - 2 \rfloor \)[/tex], let's follow the steps methodically:
1. Substitute [tex]\( x = 5.9 \)[/tex] into the expression inside the floor function:
[tex]\[
x - 2 = 5.9 - 2
\][/tex]
[tex]\[
x - 2 = 3.9
\][/tex]
2. Apply the floor function to the result:
The floor function, denoted by [tex]\(\lfloor \cdot \rfloor\)[/tex], takes a real number and rounds it down to the nearest integer.
[tex]\[
\lfloor 3.9 \rfloor = 3
\][/tex]
3. Multiply the result of the floor function by 3:
[tex]\[
3 \times \lfloor 3.9 \rfloor = 3 \times 3 = 9
\][/tex]
Thus, the value of [tex]\( f(5.9) \)[/tex] is:
[tex]\[
f(5.9) = 9
\][/tex]
Hence, the correct answer is [tex]\( 9 \)[/tex].
