To determine [tex]\( f(7.6) \)[/tex] given the function [tex]\( f(x) = \frac{1}{2} \lfloor x \rfloor \)[/tex], let's go through the process step-by-step:
1. Identify the floor value of [tex]\( x \)[/tex]: The floor function, denoted by [tex]\( \lfloor x \rfloor \)[/tex], takes any real number [tex]\( x \)[/tex] and gives the greatest integer that is less than or equal to [tex]\( x \)[/tex]. Thus, for [tex]\( x = 7.6 \)[/tex]:
[tex]\[
\lfloor 7.6 \rfloor = 7
\][/tex]
2. Substitute the floor value into the function [tex]\( f(x) \)[/tex]: Since [tex]\( f(x) = \frac{1}{2} \lfloor x \rfloor \)[/tex], we substitute [tex]\( \lfloor 7.6 \rfloor = 7 \)[/tex] into the function:
[tex]\[
f(7.6) = \frac{1}{2} \cdot 7
\][/tex]
3. Perform the multiplication:
[tex]\[
f(7.6) = \frac{1}{2} \cdot 7 = \frac{7}{2} = 3.5
\][/tex]
Therefore, [tex]\( f(7.6) = 3.5 \)[/tex].
So, the correct answer is:
[tex]\[
\boxed{3.5}
\][/tex]
