Certainly! Let's solve the given problem step-by-step.
We are given:
1. A set of ordered pairs representing the values of the function [tex]\( g \)[/tex]:
[tex]\[ g = \{(-5, -1), (0, 6), (2, -9), (5, 2)\} \][/tex]
2. A linear function [tex]\( h(x) \)[/tex]:
[tex]\[ h(x) = 2x - 3 \][/tex]
We need to find the following:
### 1. The value of [tex]\( g(2) \)[/tex]
To find [tex]\( g(2) \)[/tex], we look for the ordered pair in the set [tex]\( g \)[/tex] where the first element is [tex]\( 2 \)[/tex]. From the given set [tex]\( g \)[/tex]:
[tex]\[ g = \{(-5, -1), (0, 6), (2, -9), (5, 2)\} \][/tex]
We locate the pair where the first element is [tex]\( 2 \)[/tex]:
[tex]\[
(2, -9)
\][/tex]
Thus, the value of [tex]\( g(2) \)[/tex] is:
[tex]\[
g(2) = -9
\][/tex]
### 2. The value of [tex]\( h(4) \)[/tex]
Next, we need to find [tex]\( h(4) \)[/tex] using the function [tex]\( h(x) = 2x - 3 \)[/tex].
Substitute [tex]\( x = 4 \)[/tex] into the function:
[tex]\[
h(4) = 2(4) - 3 = 8 - 3 = 5
\][/tex]
Thus, the value of [tex]\( h(4) \)[/tex] is:
[tex]\[
h(4) = 5
\][/tex]
### Summary
Putting it all together, we have:
- The value of [tex]\( g(2) \)[/tex] is [tex]\( -9 \)[/tex].
- The value of [tex]\( h(4) \)[/tex] is [tex]\( 5 \)[/tex].
Therefore, the final results are:
[tex]\[
g(2) = -9 \quad \text{and} \quad h(4) = 5
\][/tex]
