To evaluate [tex]\( g(t) = |5 - t| \)[/tex] for the given values of [tex]\( t \)[/tex], we'll proceed step by step for each specific value.
### a) Evaluation of [tex]\( g(8) \)[/tex]:
1. Start with the function [tex]\( g(t) = |5 - t| \)[/tex].
2. Substitute [tex]\( t = 8 \)[/tex] into the function:
[tex]\[
g(8) = |5 - 8|
\][/tex]
3. Compute the expression inside the absolute value:
[tex]\[
5 - 8 = -3
\][/tex]
4. Find the absolute value of [tex]\(-3\)[/tex]:
[tex]\[
|-3| = 3
\][/tex]
5. Therefore, the value of [tex]\( g(8) \)[/tex] is:
[tex]\[
g(8) = 3
\][/tex]
### b) Evaluation of [tex]\( g(37) \)[/tex]:
1. Start with the function [tex]\( g(t) = |5 - t| \)[/tex].
2. Substitute [tex]\( t = 37 \)[/tex] into the function:
[tex]\[
g(37) = |5 - 37|
\][/tex]
3. Compute the expression inside the absolute value:
[tex]\[
5 - 37 = -32
\][/tex]
4. Find the absolute value of [tex]\(-32\)[/tex]:
[tex]\[
|-32| = 32
\][/tex]
5. Therefore, the value of [tex]\( g(37) \)[/tex] is:
[tex]\[
g(37) = 32
\][/tex]
In conclusion:
[tex]\[
\text{a) } g(8) = 3
\][/tex]
[tex]\[
\text{b) } g(37) = 32
\][/tex]
