If f(x) and g(x) are polynomial functions of x, then domain of `(f(x))/(g(x))` is

Options

A. `(-oo, 0]`
B. `[0, oo)`
C. R
D. R - {g(x) = 0}

Answer

To find the domain of the function \( \frac{f(x)}{g(x)} \), where \( f(x) \) and \( g(x) \) are polynomial functions, we need to consider the conditions under which this function is defined.

### Step-by-Step Solution:

1. **Understanding Polynomials**:
- A polynomial function \( f(x) \) is defined for all real numbers. This means that \( f(x) \) can take any real value of \( x \) without any restrictions.

2. **Identifying the Denominator**:
- The function \( \frac{f(x)}{g(x)} \) is a rational function, which is defined as long as the denominator \( g(x) \) is not equal to zero.

3. **Finding the Points Where \( g(x) = 0 \)**:
- To determine the domain of \( \frac{f(x)}{g(x)} \), we need to find the values of \( x \) for which \( g(x) = 0 \). These values will be excluded from the domain.

4. **Setting Up the Equation**:
- Solve the equation \( g(x) = 0 \). The solutions to this equation will give us the points where the function is undefined.

5. **Defining the Domain**:
- The domain of the function \( \frac{f(x)}{g(x)} \) will be all real numbers except for the values of \( x \) that make \( g(x) = 0 \).

6. **Conclusion**:
- Therefore, the domain of \( \frac{f(x)}{g(x)} \) is:
\[ \text{Domain} = \{ x \in \mathbb{R} \mid g(x) \neq 0 \} \]

### Final Answer:
The domain of \( \frac{f(x)}{g(x)} \) is all real numbers except where \( g(x) = 0 \).

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