To find the larger solution in the solution set of \( f(x) = g(x) \), you need to identify the x-values where the graphs of the functions intersect. Based on the points you've provided, which are \( (-3, 4) \) and \( (4, 11) \), we can see that these points represent where \( f \) and \( g \) have the same y-value, meaning:
- At \( x = -3 \), both \( f(-3) = 4 \) and \( g(-3) = 4 \).
- At \( x = 4 \), both \( f(4) = 11 \) and \( g(4) = 11 \).
Among the x-values where the functions are equal, the larger solution is \( x = 4 \).
Therefore, the largest solution in the solution set of \( f(x) = g(x) \) is:
\[ \boxed{4} \]