Alright, let's break down the problem step by step.
We are given the conditions:
[tex]\[ j = h \][/tex]
[tex]\[ k = m \][/tex]
We need to find which expression correctly represents [tex]\( g \)[/tex].
Let's examine each option:
1. [tex]\( g = \frac{f}{2} \)[/tex]:
- This expression involves the variable [tex]\( f \)[/tex]. We have no information on how [tex]\( f \)[/tex] relates to [tex]\( j \)[/tex], [tex]\( h \)[/tex], [tex]\( k \)[/tex], or [tex]\( m \)[/tex], so we cannot determine if this expression correctly represents [tex]\( g \)[/tex] based on the given conditions.
2. [tex]\( g = 2f \)[/tex]:
- Similar to the first option, this expression involves [tex]\( f \)[/tex]. Without any information linking [tex]\( f \)[/tex] to [tex]\( j \)[/tex], [tex]\( h \)[/tex], [tex]\( k \)[/tex], or [tex]\( m \)[/tex], we cannot verify if this expression represents [tex]\( g \)[/tex].
3. [tex]\( g = \frac{j}{h} \)[/tex]:
- Given that [tex]\( j = h \)[/tex], substituting [tex]\( h \)[/tex] for [tex]\( j \)[/tex] in the expression yields:
[tex]\[
g = \frac{j}{h} = \frac{h}{h} = 1
\][/tex]
- This simplifies to [tex]\( g = 1 \)[/tex], which is a constant value and thus a valid expression based on the given condition.
4. [tex]\( g = \frac{k}{m} \)[/tex]:
- Similarly, given that [tex]\( k = m \)[/tex], substituting [tex]\( m \)[/tex] for [tex]\( k \)[/tex] in the expression yields:
[tex]\[
g = \frac{k}{m} = \frac{m}{m} = 1
\][/tex]
- This also simplifies to [tex]\( g = 1 \)[/tex], indicating that this is a valid expression as well.
Both options 3 and 4 simplify to [tex]\( g = 1 \)[/tex], which is a straightforward and valid expression given the conditions [tex]\( j = h \)[/tex] and [tex]\( k = m \)[/tex].
Therefore, the correct answers are:
[tex]\[ g = \frac{j}{h} \][/tex]
[tex]\[ g = \frac{k}{m} \][/tex]
However, since the question likely expects a single choice, we select one of the two correct expressions:
[tex]\[ g = \frac{j}{h} \][/tex]
So, the correct option is:
[tex]\[ \boxed{g = \frac{j}{h}} \][/tex]
