`{:("Column A" , "The functons f and g are defined as","ColumnB"),(, f(x,y) = 2x + y and g(x,y) = x + 2y,),( f(4,3), ,g(4,3)):}`

Options

A. If column A is larger
B. If column B is larger
C. If the columns are equal
D. If there is not enough information to decide

Answer

To solve the problem, we need to evaluate the functions \( f \) and \( g \) at the point \( (4, 3) \).

### Step-by-Step Solution:

1. **Identify the Functions**:
- The functions are given as:
\[ f(x, y) = 2x + y \]
\[ g(x, y) = x + 2y \]

2. **Evaluate \( f(4, 3) \)**:
- Substitute \( x = 4 \) and \( y = 3 \) into the function \( f \):
\[ f(4, 3) = 2(4) + 3 \]
- Calculate:
\[ = 8 + 3 = 11 \]

3. **Evaluate \( g(4, 3) \)**:
- Substitute \( x = 4 \) and \( y = 3 \) into the function \( g \):
\[ g(4, 3) = 4 + 2(3) \]
- Calculate:
\[ = 4 + 6 = 10 \]

4. **Compare the Results**:
- From the calculations, we have:
- \( f(4, 3) = 11 \) (Column A)
- \( g(4, 3) = 10 \) (Column B)
- Therefore, we can conclude that:
\[ f(4, 3) > g(4, 3) \]

5. **Final Conclusion**:
- Since \( 11 > 10 \), we can say that the value in Column A is greater than the value in Column B.

### Summary:
- The value of Column A (which is \( f(4, 3) \)) is 11.
- The value of Column B (which is \( g(4, 3) \)) is 10.
- Thus, Column A is larger than Column B.