If `f(x)=3^(1+x)," then "f(x)f(y)f(z)` is equal to

Options

A. `f(x+y+z)`
B. `f(x+y+z+1)`
C. `f(x+y+z+2)`
D. `f(x+y+z+3)`

Explanation

To solve the problem, we need to find the value of \( f(x)f(y)f(z) \) given that \( f(x) = 3^{1+x} \).

### Step-by-Step Solution:

1. **Identify the Function:**
We have the function defined as:
\[ f(x) = 3^{1+x} \]

2. **Calculate \( f(y) \) and \( f(z) \):**
Using the same function definition:
\[ f(y) = 3^{1+y} \]
\[ f(z) = 3^{1+z} \]

3. **Multiply the Functions:**
We need to find \( f(x)f(y)f(z) \):
\[ f(x)f(y)f(z) = (3^{1+x})(3^{1+y})(3^{1+z}) \]

4. **Combine the Exponents:**
When multiplying powers with the same base, we can add the exponents:
\[ f(x)f(y)f(z) = 3^{(1+x) + (1+y) + (1+z)} \]

5. **Simplify the Exponent:**
Now, simplify the exponent:
\[ (1+x) + (1+y) + (1+z) = 1 + 1 + 1 + x + y + z = 3 + x + y + z \]

6. **Final Expression:**
Thus, we have:
\[ f(x)f(y)f(z) = 3^{3 + x + y + z} \]

### Conclusion:
The final result is:
\[ f(x)f(y)f(z) = 3^{x+y+z+3} \]