If `f(x)=e^x` and `g(x)=(log)_e x(x >0),` find `foga n dgofdot` Is `fog=gof?`

Explanation

To solve the problem step by step, we need to find \( f(g(x)) \) and \( g(f(x)) \) for the given functions \( f(x) = e^x \) and \( g(x) = \log_e x \) (where \( x > 0 \)). We will also determine if \( f(g(x)) = g(f(x)) \).

### Step 1: Find \( f(g(x)) \)

1. Start with the function \( g(x) = \log_e x \).
2. Substitute \( g(x) \) into \( f(x) \):
\[
f(g(x)) = f(\log_e x) = e^{\log_e x}
...