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

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Answer 1 · 2015-07-02T06:53:14

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

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

$x^2 = (11-y)/3$ .

But for every value of $y$ except $y=11$ , there are two possible values of $x$ , namely $+-sqrt ((11-y)/3)$ .

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

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