Sure, let's solve the problem step-by-step.
Part (a) \( g(4.2) \)
Given the function \( g(x) = \frac{x}{2} + 7 \), we need to find the value of \( g \) at \( x = 4.2 \).
1. Substitute \( x = 4.2 \) into the function \( g(x) = \frac{x}{2} + 7 \).
2. Calculate \( \frac{4.2}{2} \):
[tex]\[
\frac{4.2}{2} = 2.1
\][/tex]
3. Add 7 to this result:
[tex]\[
2.1 + 7 = 9.1
\][/tex]
Therefore, \( g(4.2) = 9.1 \).
Part (b) \( g(-4.2) \)
Again, using the function \( g(x) = \frac{x}{2} + 7 \), we need to find the value of \( g \) at \( x = -4.2 \).
1. Substitute \( x = -4.2 \) into the function \( g(x) = \frac{x}{2} + 7 \).
2. Calculate \( \frac{-4.2}{2} \):
[tex]\[
\frac{-4.2}{2} = -2.1
\][/tex]
3. Add 7 to this result:
[tex]\[
-2.1 + 7 = 4.9
\][/tex]
Therefore, \( g(-4.2) = 4.9 \).
So, the final results are:
- \( g(4.2) = 9.1 \)
- [tex]\( g(-4.2) = 4.9 \)[/tex]
