If `f(x)=e^(x)` and `g(x)=(x)/(2)`, then `g(f(2))=`

Options

A. `2.7`
B. `3.7`
C. `4.2`
D. `5.4`

Explanation

To solve the problem, we need to find the value of \( g(f(2)) \) given the functions \( f(x) = e^x \) and \( g(x) = \frac{x}{2} \).

### Step-by-Step Solution:

1. **Calculate \( f(2) \)**:
\[ f(2) = e^2 \]
Here, we substitute \( x \) with \( 2 \) in the function \( f(x) \).

2. **Evaluate \( e^2 \)**:
The value of \( e^2 \) is approximately \( 7.389 \). This is a constant value that can be found using a scientific calculator or a mathematical table.

3. **Substitute \( f(2) \) into \( g(x) \)**:
Now we need to find \( g(f(2)) \), which is:
\[ g(f(2)) = g(e^2) \]

4. **Calculate \( g(e^2) \)**:
Using the function \( g(x) = \frac{x}{2} \), we substitute \( e^2 \):
\[ g(e^2) = \frac{e^2}{2} \]

5. **Evaluate \( g(e^2) \)**:
Substituting the approximate value of \( e^2 \):
\[ g(e^2) = \frac{7.389}{2} \approx 3.6945 \]

6. **Final Answer**:
Therefore, the value of \( g(f(2)) \) is approximately:
\[ g(f(2)) \approx 3.6945 \]

### Summary:
The value of \( g(f(2)) \) is approximately \( 3.6945 \).