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

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^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.

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