If `f(x)=e^(x)`, then the value of 7 f (x) will be equal to

Options

A. `e^(7x)`
B. `7e^(x)`
C. `7e^(7x)`
D. `e^(x)`

Answer

To solve the problem, we need to find the value of \( 7f(x) \) given that \( f(x) = e^x \).

### Step-by-Step Solution:

1. **Identify the function**: We know that \( f(x) = e^x \).

2. **Substitute \( f(x) \) into \( 7f(x) \)**: We need to calculate \( 7f(x) \).
\[ 7f(x) = 7 \cdot f(x) = 7 \cdot e^x \]

3. **Simplify the expression**: The expression simplifies to:
\[ 7f(x) = 7e^x \]

4. **Identify the correct option**: Now we compare \( 7e^x \) with the given options:
- Option 1: \( e^{7x} \)
- Option 2: \( 7e^x \)
- Option 3: \( 7e^{7x} \)
- Option 4: \( e^x \)

The correct option that matches our result \( 7e^x \) is **Option 2**.

### Final Answer:
The value of \( 7f(x) \) is \( 7e^x \).

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