To find the value of [tex]\( f(7.6) \)[/tex] for the function [tex]\( f(x) = \frac{1}{2} \lfloor x \rfloor \)[/tex], follow these steps:
1. Understand the floor function: The floor function, denoted as [tex]\( \lfloor x \rfloor \)[/tex], gives the greatest integer less than or equal to [tex]\( x \)[/tex].
2. Calculate the floor value of [tex]\( x \)[/tex]: For [tex]\( x = 7.6 \)[/tex], the greatest integer less than or equal to 7.6 is 7. Thus, [tex]\( \lfloor 7.6 \rfloor = 7 \)[/tex].
3. Substitute into the function: Now that we know [tex]\( \lfloor 7.6 \rfloor = 7 \)[/tex], substitute this value 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. Simplify the expression: Perform the arithmetic operation.
[tex]\[
\frac{1}{2} \times 7 = 3.5
\][/tex]
Therefore, the value of [tex]\( f(7.6) \)[/tex] is [tex]\( 3.5 \)[/tex].
