Question 1209618
Here's how to determine if f(x) has an inverse and find f⁻¹(0) if it does:

1. **Check if f(x) is one-to-one:**

A function has an inverse if and only if it is one-to-one (injective), meaning that every element in the range corresponds to exactly one element in the domain.  A simple way to check if a function is one-to-one is to see if it passes the horizontal line test.  If any horizontal line intersects the graph of the function more than once, the function is not one-to-one and does not have an inverse.

Our function is f(x) = x² + (9/5)x - 4.  This is a quadratic function, and its graph is a parabola. Parabolas fail the horizontal line test (except for very special cases where the domain is restricted to only one side of the vertex).  Since this is a parabola, it is not one-to-one.

2. **Conclusion:**

Since f(x) is not one-to-one, it does not have an inverse.

Therefore, f⁻¹(0) is *undef*.