IDNLearn.com offers a collaborative platform for sharing and gaining knowledge. Find the information you need quickly and easily with our reliable and thorough Q&A platform.
Sagot :
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].
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].
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. IDNLearn.com has the solutions you’re looking for. Thanks for visiting, and see you next time for more reliable information.