



 
Hi Elliot. The inverse of a function f is a function g such that g(f(x)) = x. So if you have the function f(x) = ax^{2} + bx + c (a general quadratic function), then g(f(x)) must give you the original value x. You should already see the problem: there will be two functions, not one, since a function must provide a unique value in its range for each value in its domain and a quadratic maps two values to one (for example, 2^{2} = (2)^{2} = 4).
But this maps two range values to a single domain value, so it isn't actually a function. The inverse of the quadratic is the curve formed by the union of the following two functions: Cheers,  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 