If `f(x)=e^x,` then what should be `(fofof) (x)`

Options

A. `e^(e^(e^(x)))`
B. `e^(e^(x))`
C. `e^(e^(e^(x)))`
D. none of these

Answer

To solve the problem, we need to find \((fofof)(x)\) given that \(f(x) = e^x\).

### Step-by-Step Solution:

1. **Understand the Function**: We have \(f(x) = e^x\).

2. **Find \(f(f(x))\)**:
- First, we need to find \(f(f(x))\).
- Substitute \(f(x)\) into itself:
\[ f(f(x)) = f(e^x) \]
- Now apply the function \(f\) to \(e^x\):
\[ f(e^x) = e^{e^x} \]

3. **Find \(f(f(f(x)))\)**:
- Now we need to find \(f(f(f(x)))\) or \(f(f(f(x)))\).
- Substitute \(f(f(x))\) into \(f\):
\[ f(f(f(x))) = f(e^{e^x}) \]
- Now apply the function \(f\) to \(e^{e^x}\):
\[ f(e^{e^x}) = e^{e^{e^x}} \]

4. **Final Result**:
- Therefore, \((fofof)(x) = e^{e^{e^x}}\).

### Conclusion:
The final answer is:
\[ (fofof)(x) = e^{e^{e^x}} \]