jmc

Functions that aren't invertible can be made invertible by restricting their domains. For example, the function $x^2$ is invertible if we restrict $x$ to the interval $[0,\infty )$, or to any subset of that interval. In that case, the inverse function is $\sqrt{x}$. (We could also restrict $x^2$ to the domain $(-\infty ,0]$, in which case the inverse function would be $-\sqrt{x}$.)

Similarly, by restricting the domain of the function $f(x)=2x^2-4x-5$ to an interval, we can make it invertible. What is the largest such interval that includes the point $x=0$?