# What function is the inverse of a quadratic function?

If the quadratic function is f(x) = ax^2 + bx + c then its inverse isf'(x) = [-b + +/- sqrt{b^2 - 4*(c - x)}]/(2a)

The square function.

### When can a quadratic function have an inverse?

It depends on the domain and codomain. In complex numbers, that is, when the domain and codomain are both C, every quadratic always has an inverse. If the range of the quadratic in the form ax2 + bx + c = 0 is the set of real numbers, R, then the function has an inverse if (a) b2 - 4ac ≥ 0 and (b) the range of the inverse is defined as x ≥ 0…