Given that [tex]\( g \)[/tex] is inversely proportional to [tex]\( m \)[/tex], we have the relationship
[tex]\[
g \propto \frac{1}{m}
\][/tex]
This can be written as:
[tex]\[
g = \frac{k}{m}
\][/tex]
where [tex]\( k \)[/tex] is a constant.
We are given that when [tex]\( m = 4 \)[/tex], [tex]\( g = 4.2 \)[/tex]. Using these values, we can find [tex]\( k \)[/tex]:
[tex]\[
4.2 = \frac{k}{4}
\][/tex]
Multiplying both sides by 4 to solve for [tex]\( k \)[/tex]:
[tex]\[
k = 4.2 \times 4 = 16.8
\][/tex]
Now, we need to find the value of [tex]\( g \)[/tex] when [tex]\( m = 3 \)[/tex]. Using the formula [tex]\( g = \frac{k}{m} \)[/tex]:
[tex]\[
g = \frac{16.8}{3}
\][/tex]
Dividing 16.8 by 3 gives us:
[tex]\[
g = 5.6
\][/tex]
Therefore, the value of [tex]\( g \)[/tex] when [tex]\( m = 3 \)[/tex] is
[tex]\[
\boxed{5.6}
\][/tex]
