Let a function of 2 variables be defined by `g(x, y)=xy+3xy^(2)-(x-y^(2))`, what is the value of `g(2, -1)`?

Answer

To find the value of the function \( g(x, y) = xy + 3xy^2 - (x - y^2) \) at the point \( (2, -1) \), we will substitute \( x = 2 \) and \( y = -1 \) into the function and simplify step by step.

### Step-by-Step Solution:

1. **Substitute the values into the function:**
\[ g(2, -1) = (2)(-1) + 3(2)(-1)^2 - (2 - (-1)^2) \]

2. **Calculate each term:**
- The first term:
\[ (2)(-1) = -2 \]
- The second term:
\[ 3(2)(-1)^2 = 3(2)(1) = 6 \]
- The third term:
\[ - (2 - (-1)^2) = - (2 - 1) = - (2 - 1) = -1 \]

3. **Combine the results:**
\[ g(2, -1) = -2 + 6 - 1 \]

4. **Simplify the expression:**
- First, combine \( -2 + 6 \):
\[ -2 + 6 = 4 \]
- Then, subtract \( 1 \):
\[ 4 - 1 = 3 \]

5. **Final result:**
\[ g(2, -1) = 3 \]

### Conclusion:
The value of \( g(2, -1) \) is \( 3 \).