# How do you find the inverse of #y=x^(2)-6x+4# and is it a function?

The inverse fun. of the given fun. does not exist.

Therefore, we can not find its inverse function.

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To find the inverse of ( y = x^2 - 6x + 4 ), follow these steps:

- Replace ( y ) with ( x ) and ( x ) with ( y ) in the given equation to obtain the inverse function.
- Solve the resulting equation for ( y ).
- If the resulting equation is a function, then it is the inverse of the original function.

Starting with the given function ( y = x^2 - 6x + 4 ):

[ x = y^2 - 6y + 4 ]

Now, solve for ( y ):

[ x = y^2 - 6y + 4 ] [ x - 4 = y^2 - 6y ] [ y^2 - 6y = x - 4 ] [ y^2 - 6y + 9 = x - 4 + 9 ] [ (y - 3)^2 = x + 5 ] [ y - 3 = \pm \sqrt{x + 5} ] [ y = 3 \pm \sqrt{x + 5} ]

Therefore, the inverse function is ( y = 3 \pm \sqrt{x + 5} ). Since this equation has two possible outputs for each input, it fails the vertical line test, indicating that it is not a function. Therefore, the inverse of ( y = x^2 - 6x + 4 ) is not a function.

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