To find the value of [tex]\( g(7) \)[/tex] for the function [tex]\( g(x) = \frac{7}{8} x - \frac{1}{2} \)[/tex], we need to substitute [tex]\( x = 7 \)[/tex] into the function and simplify the expression step by step:
1. Start with the function:
[tex]\[
g(x) = \frac{7}{8} x - \frac{1}{2}
\][/tex]
2. Substitute [tex]\( x = 7 \)[/tex] into the function:
[tex]\[
g(7) = \frac{7}{8} \cdot 7 - \frac{1}{2}
\][/tex]
3. Calculate [tex]\( \frac{7}{8} \cdot 7 \)[/tex]:
[tex]\[
\frac{7}{8} \cdot 7 = \frac{49}{8}
\][/tex]
4. Now subtract [tex]\( \frac{1}{2} \)[/tex] from [tex]\( \frac{49}{8} \)[/tex]. To do this, we need a common denominator:
[tex]\[
\frac{1}{2} = \frac{4}{8}
\][/tex]
5. Perform the subtraction:
[tex]\[
\frac{49}{8} - \frac{4}{8} = \frac{49 - 4}{8} = \frac{45}{8}
\][/tex]
6. Therefore, the value of [tex]\( g(7) \)[/tex] is:
[tex]\[
g(7) = \frac{45}{8}
\][/tex]
Looking at the given options, the correct answer is:
[tex]\[
\boxed{\frac{45}{8}}
\][/tex]
