Give a restriction on the function y=f(x)=ax^{2}+bx+c so that its inverse f^{-1} exists, is either strictly increasing throughout its domain, or strictly decreasing, and so that no larger domain possesses these properties.
Give a restriction on the function y=f(x)=ax^{2}+bx+c so that its inverse f^{-1} exists, is either strictly increasing throughout its domain, or strictly decreasing, and so that no larger domain possesses these properties.
Inverse functions only exist when the original function is one-to-one. Since it's a quadratic, it will be one-to-one (and in this case, strictly increasing/decreasing) from the turning point on in either direction (but not both).