Consider a quadratic function of the form f(x) = b (x−h / a )^2+ k for real numbers a, b, h, k, and a, b ≠ 0.
a. explain why quadratic functions never have an inverse without restricting the domain.
b. what are the coordinates of the vertex of the graph of f?
c. state the possible domains you can restrict f on so that it has an inverse.
d. what kind of function is the inverse of a quadratic function on an appropriate domain?
e. find f^−1 for each of the domains you gave in part (c).