If `f(x)=e^(x)`, and `g(x)=log_(e )x`, then value of fog will be

Options

A. x
B. 0
C. 1
D. e

Answer

To find the value of \( f(g(x)) \) where \( f(x) = e^x \) and \( g(x) = \log_e x \), we will follow these steps:

### Step 1: Understand the composition of functions
We need to find \( f(g(x)) \), which means we will substitute \( g(x) \) into \( f(x) \).

### Step 2: Substitute \( g(x) \) into \( f(x) \)
Given:
- \( g(x) = \log_e x \)
- \( f(x) = e^x \)

Now, we can write:
\[ f(g(x)) = f(\log_e x) \]

### Step 3: Apply the function \( f \) to \( g(x) \)
Now, we substitute \( \log_e x \) into \( f(x) \):
\[ f(\log_e x) = e^{\log_e x} \]

### Step 4: Simplify \( e^{\log_e x} \)
Using the property of logarithms and exponents, we know that:
\[ e^{\log_e x} = x \]

### Step 5: Conclusion
Thus, we find that:
\[ f(g(x)) = x \]

### Final Answer
The value of \( f(g(x)) \) is \( x \).

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