f(x) = 2(x-1)^2 - 7
So, if we restrict the domain to x>1 or x<1 we can find an inverse
I expect you can turn that info into an interval . . .
Some 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,\inf), 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 (-\inf,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?
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