Let's solve the problem step by step:
We are given two functions:
[tex]\[ f(x) = \frac{x - 1}{2} \][/tex]
[tex]\[ g(x) = 3x + 1 \][/tex]
We need to evaluate [tex]\( f\left(\frac{-1}{2}\right) + 1 \)[/tex].
1. Evaluate [tex]\( f\left(\frac{-1}{2}\right) \)[/tex]:
Substitute [tex]\( x = -\frac{1}{2} \)[/tex] into the function [tex]\( f(x) \)[/tex]:
[tex]\[ f\left(\frac{-1}{2}\right) = \frac{\left(\frac{-1}{2}\right) - 1}{2} \][/tex]
Simplify the expression inside the parentheses:
[tex]\[ f\left(\frac{-1}{2}\right) = \frac{-\frac{1}{2} - 1}{2} \][/tex]
Convert 1 to a fraction with a common denominator:
[tex]\[ f\left(\frac{-1}{2}\right) = \frac{-\frac{1}{2} - \frac{2}{2}}{2} \][/tex]
[tex]\[ f\left(\frac{-\frac{3}{2}}{2}\right) \][/tex]
Simplify the numerator:
[tex]\[ f\left(\frac{-1}{2}\right) = \frac{-\frac{3}{2}}{2} \][/tex]
Further simplify the fraction:
[tex]\[ f\left(\frac{-1}{2}\right) = -\frac{3}{4} \][/tex]
2. Add 1 to the result of [tex]\( f\left(\frac{-1}{2}\right) \)[/tex]:
We found [tex]\( f\left(\frac{-1}{2}\right) = -0.75 \)[/tex].
Now, add 1 to [tex]\(-0.75\)[/tex]:
[tex]\[ -0.75 + 1 = 0.25 \][/tex]
Therefore, the final result is [tex]\(\boxed{0.25}\)[/tex].
