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Given the function [tex] g [/tex] defined by the formula [tex] g(x) = \frac{x-5}{2} [/tex], find the following:

(a) [tex] g(9) [/tex]

(b) [tex] g(0) [/tex]

(c) [tex] g(3) [/tex]

(d) [tex] g(17) [/tex]

Sagot :

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.