# Math Help - inverse functions

1. ## inverse functions

i need to find the inverse of f(x) = x^2-4x+3 how do you do it when you have x^2 and x?

2. Originally Posted by katt
i need to find the inverse of f(x) = x^2-4x+3 how do you do it when you have x^2 and x?
complete the square.

3. Y=x^2-4x+3 => x^2-4x+3-y=0

delta'=4-3+y=1+y

=> x1=2+squareroot(1+y)
and x2=2-squareroot(1-y)

this is the inverse you choose x1 or x2 depending on the constrains given .

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

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

$y = (x - 2)^2 - 1$

swap x and y ...

$x = (y - 2)^2 - 1$

$x + 1 = (y - 2)^2$

$\pm \sqrt{x+1} = y - 2$

$y = 2 \pm \sqrt{x+1}$

restrict the domain of the original function to $x \ge 2$, and the inverse function is $f^{-1}(x) = 2 + \sqrt{x+1}
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