To reflect the function \( f(x) = \frac{1}{-x^2} + x \) over the y-axis, we need to replace \( x \) with \( -x \) in the function.
Starting with the function: \[ f(x) = \frac{1}{-x^2} + x \]
We substitute \( -x \) for \( x \): \[ g(x) = f(-x) = \frac{1}{-(-x)^2} + (-x) \]
Simplifying this: \[ g(x) = \frac{1}{-x^2} - x \]
Thus, the final expression for the reflected function \( g(x) \) is: \[ g(x) = \frac{1}{-x^2} - x \]
In the form you provided, to fill in the blanks: \[ G(x) = \frac{1}{-x^2} + (-1)x \]
So, the completed expression would be: \[ G(x) = \frac{1}{-x^2} - x \]
Therefore, the answers to fill in the blanks are:
- The blank for the first term: \(-\)
- The blank for the second term: \(-1\)