Let's solve the problem step by step.
Given the function [tex]\( f(x) = \frac{1}{2} \lfloor x \rfloor \)[/tex], we need to determine [tex]\( f(7.6) \)[/tex].
1. Understand the floor function: The floor function [tex]\(\lfloor x \rfloor\)[/tex] gives the greatest integer less than or equal to [tex]\( x \)[/tex].
2. Apply the floor function to 7.6:
[tex]\[
\lfloor 7.6 \rfloor = 7
\][/tex]
3. Substitute [tex]\(\lfloor 7.6 \rfloor\)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(7.6) = \frac{1}{2} \lfloor 7.6 \rfloor = \frac{1}{2} \times 7
\][/tex]
4. Compute the result:
[tex]\[
\frac{1}{2} \times 7 = 3.5
\][/tex]
Thus, [tex]\( f(7.6) = 3.5 \)[/tex].
So, the correct answer is:
[tex]\[ 3.5 \][/tex]
