If `f(x)=log(1+x)andg(x)=e^(x)`, then the value of (gof) (x) is :

Options

A. `e^(1+x)`
B. `1+x`
C. `logx`
D. None of these

Answer

To find the value of \( (g \circ f)(x) \), we need to evaluate the composition of the functions \( f(x) \) and \( g(x) \).

### Step-by-Step Solution:

1. **Identify the Functions**:
- We have \( f(x) = \log(1+x) \)
- We have \( g(x) = e^x \)

2. **Write the Composition**:
- The composition \( (g \circ f)(x) \) means we need to evaluate \( g(f(x)) \).
- This can be expressed as \( g(f(x)) = g(\log(1+x)) \).

3. **Substitute \( f(x) \) into \( g(x) \)**:
- Now, substitute \( f(x) \) into \( g(x) \):
\[ g(f(x)) = g(\log(1+x)) = e^{\log(1+x)} \]

4. **Use the Exponential and Logarithm Property**:
- We know from logarithmic properties that \( e^{\log(a)} = a \) for any \( a > 0 \).
- Applying this property here gives:
\[ e^{\log(1+x)} = 1+x \]

5. **Final Result**:
- Therefore, the value of \( (g \circ f)(x) \) is:
\[ (g \circ f)(x) = 1 + x \]

### Conclusion:
The final answer is \( (g \circ f)(x) = 1 + x \).