If `f(x)=5x^(3) and g(x)=3x^(5)`, then `f(x).g(x)` will be

Options

A. Even function
B. Odd function
C. Both
D. None of these

Answer

To solve the problem, we need to find the product of the functions \( f(x) \) and \( g(x) \).

1. **Identify the functions**:
- We have \( f(x) = 5x^3 \)
- We have \( g(x) = 3x^5 \)

2. **Multiply the functions**:
- To find \( f(x) \cdot g(x) \), we multiply the two functions together:
\[ f(x) \cdot g(x) = (5x^3) \cdot (3x^5) \]

3. **Combine the coefficients**:
- Multiply the coefficients (5 and 3):
\[ 5 \cdot 3 = 15 \]

4. **Combine the powers of \( x \)**:
- When multiplying powers of the same base, we add the exponents:
\[ x^3 \cdot x^5 = x^{3+5} = x^8 \]

5. **Final expression**:
- Now, combine the coefficient and the power of \( x \):
\[ f(x) \cdot g(x) = 15x^8 \]

Thus, the final result is:
\[ f(x) \cdot g(x) = 15x^8 \]