Whats the inverse function of f(x)=x²-4x+3?

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Answer 1 · 2018-04-10T21:09:51

So you have the equation $y=x^2-4x+3$

Swap $y$ with $x$ and vice versa

$x=y^2-4y+3$

Solve for $y$

$y^2-4y=x-3$
$(y-2)(y-2)-2=x-3$
$(y-2)^2-2=x-3$
$(y-2)^2=x-1$
$y-2=+-sqrt(x-1)$
$y=2+-sqrt(x-1)$

Now swap $y$ with $f^-1(x)$

$f^-1(x)=2+-sqrt(x-1)$