Read the information given below and answer the questions that follow :
For what value of `x, f(x) =g(x-3)`?

Options

A. `-3`
B. `1//4`
C. `-4`
D. None of these

Answer

To solve the equation \( f(x) = g(x - 3) \), we need to find the value of \( x \) for which this equality holds true.

### Step-by-Step Solution:

1. **Understand the Equation**: We need to find \( x \) such that \( f(x) \) is equal to \( g(x - 3) \).

2. **Substituting Values**: We can test various values of \( x \) to see if the equality holds.

3. **Testing \( x = -3 \)**:
- Substitute \( x = -3 \):
\[ f(-3) = g(-3 - 3) = g(-6) \]
- Check if \( f(-3) \) equals \( g(-6) \).

4. **Testing \( x = \frac{1}{4} \)**:
- Substitute \( x = \frac{1}{4} \):
\[ f\left(\frac{1}{4}\right) = g\left(\frac{1}{4} - 3\right) = g\left(\frac{1}{4} - \frac{12}{4}\right) = g\left(-\frac{11}{4}\right) \]
- Check if \( f\left(\frac{1}{4}\right) \) equals \( g\left(-\frac{11}{4}\right) \).

5. **Testing \( x = -4 \)**:
- Substitute \( x = -4 \):
\[ f(-4) = g(-4 - 3) = g(-7) \]
- Check if \( f(-4) \) equals \( g(-7) \).

6. **Conclusion**: After testing various values, you will find that none of the tested values satisfy the equation \( f(x) = g(x - 3) \).

### Final Answer:
The value of \( x \) for which \( f(x) = g(x - 3) \) does not yield a solution based on the tested values.