What is the inverse function of f(x)=11-3x^2f(x)=11−3x2?

1 Answer
Jim H
Jul 2, 2015

The function is not one-to-one. It does not have an inverse.

Explanation:

From y = 11-3x^2y=11−3x2, if we try to solve for xx int terms of yy, we get:

x^2 = (11-y)/3x2=11−y3.

But for every value of yy except y=11y=11, there are two possible values of xx, namely +-sqrt ((11-y)/3)±√11−y3.

Functions never return 2 values. So xx is not a function of yy, and f(x)f(x) is not invertible.

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