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Question

The function f(x) = -3x^2 + 36x - 7, defined for all real numbers, does not have an inverse. However, when its domain is restricted to x [c,), the function does become invertible, for certain values of c. What is the smallest such value of c?

Accepted Answer

We can complete the square, to get f(x) = 101 - 3(x - 6)^2. Thus, the graph of f(x) is a parabola with axis of symmetry x = 6, so the smallest possible value of c is 6.