Certainly! Let's solve each part step by step using the given function [tex]\( g(x) = \frac{x - 5}{2} \)[/tex].
### Part (a) [tex]\( g(9) \)[/tex]
To find [tex]\( g(9) \)[/tex]:
1. Substitute [tex]\( x = 9 \)[/tex] into the function [tex]\( g \)[/tex]:
[tex]\[
g(9) = \frac{9 - 5}{2}
\][/tex]
2. Simplify the expression inside the parentheses:
[tex]\[
9 - 5 = 4
\][/tex]
3. Divide by 2:
[tex]\[
\frac{4}{2} = 2.0
\][/tex]
So, [tex]\( g(9) = 2.0 \)[/tex].
### Part (b) [tex]\( g(0) \)[/tex]
To find [tex]\( g(0) \)[/tex]:
1. Substitute [tex]\( x = 0 \)[/tex] into the function [tex]\( g \)[/tex]:
[tex]\[
g(0) = \frac{0 - 5}{2}
\][/tex]
2. Simplify the expression inside the parentheses:
[tex]\[
0 - 5 = -5
\][/tex]
3. Divide by 2:
[tex]\[
\frac{-5}{2} = -2.5
\][/tex]
So, [tex]\( g(0) = -2.5 \)[/tex].
### Part (c) [tex]\( g(3) \)[/tex]
To find [tex]\( g(3) \)[/tex]:
1. Substitute [tex]\( x = 3 \)[/tex] into the function [tex]\( g \)[/tex]:
[tex]\[
g(3) = \frac{3 - 5}{2}
\][/tex]
2. Simplify the expression inside the parentheses:
[tex]\[
3 - 5 = -2
\][/tex]
3. Divide by 2:
[tex]\[
\frac{-2}{2} = -1.0
\][/tex]
So, [tex]\( g(3) = -1.0 \)[/tex].
### Part (d) [tex]\( g(17) \)[/tex]
To find [tex]\( g(17) \)[/tex]:
1. Substitute [tex]\( x = 17 \)[/tex] into the function [tex]\( g \)[/tex]:
[tex]\[
g(17) = \frac{17 - 5}{2}
\][/tex]
2. Simplify the expression inside the parentheses:
[tex]\[
17 - 5 = 12
\][/tex]
3. Divide by 2:
[tex]\[
\frac{12}{2} = 6.0
\][/tex]
So, [tex]\( g(17) = 6.0 \)[/tex].
### Summary of Results
(a) [tex]\( g(9) = 2.0 \)[/tex]
(b) [tex]\( g(0) = -2.5 \)[/tex]
(c) [tex]\( g(3) = -1.0 \)[/tex]
(d) [tex]\( g(17) = 6.0 \)[/tex]
These are the values of the function [tex]\( g \)[/tex] at the given points.
