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

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

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To find the inverse function of ( f(x) = 11 - 3x^2 ), follow these steps:

- Replace ( f(x) ) with ( y ).
- Swap ( x ) and ( y ).
- Solve for ( y ).
- Replace ( y ) with ( f^{-1}(x) ).

[ y = 11 - 3x^2 ] [ x = 11 - 3y^2 ] [ 3y^2 = 11 - x ] [ y^2 = \frac{11 - x}{3} ] [ y = \pm \sqrt{\frac{11 - x}{3}} ]

Thus, the inverse function of ( f(x) = 11 - 3x^2 ) is: [ f^{-1}(x) = \pm \sqrt{\frac{11 - x}{3}} ]

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