If `f(x)=logx and g(x)=e^(x)`, then (fog) (x) is:

Options

A. `e^(x)`
B. x
C. log x
D. 1

Answer

To solve the problem, we need to find the composition of the functions \( f \) and \( g \), denoted as \( (f \circ g)(x) \).

1. **Identify the functions**:
- Given \( f(x) = \log x \)
- Given \( g(x) = e^x \)

2. **Write the composition**:
- We need to find \( (f \circ g)(x) \), which means we will substitute \( g(x) \) into \( f(x) \).
- This can be expressed as \( f(g(x)) \).

3. **Substitute \( g(x) \) into \( f(x) \)**:
- We know \( g(x) = e^x \), so we substitute this into \( f(x) \):
\[ f(g(x)) = f(e^x) \]

4. **Evaluate \( f(e^x) \)**:
- Since \( f(x) = \log x \), we replace \( x \) with \( e^x \):
\[ f(e^x) = \log(e^x) \]

5. **Use logarithmic properties**:
- We can simplify \( \log(e^x) \) using the property of logarithms that states \( \log(a^b) = b \cdot \log(a) \):
\[ \log(e^x) = x \cdot \log(e) \]
- Since \( \log(e) = 1 \), we have:
\[ \log(e^x) = x \cdot 1 = x \]

6. **Final result**:
- Therefore, \( (f \circ g)(x) = x \).

The final answer is:
\[ (f \circ g)(x) = x \]