To find \( f(f+g)(x) \), we first need to determine what \( f + g \) means in this context. Typically, when we say \( f+g \), we mean the sum of the two functions applied to \( x \).
Given:
- \( f(x) = x + 5 \)
- \( g(x) = 2 \)
Now, let's find \( (f + g)(x) \):
\[ (f + g)(x) = f(x) + g(x) \]
Substituting the expressions for \( f(x) \) and \( g(x) \):
\[ (f + g)(x) = (x + 5) + 2 = x + 7 \]
Next, we need to find \( f(f + g)(x) \), which is:
\[ f((f + g)(x)) = f(x + 7) \]
Now, we apply the function \( f \) to \( x + 7 \):
\[ f(x + 7) = (x + 7) + 5 \]
Simplifying this gives:
\[ f(x + 7) = x + 12 \]
Therefore,
\[ f(f + g)(x) = x + 12 \]
This is the final result.