What is the inverse of x^2-4x+5

Mathematics

1 answer:

lisabon 2012 [21]3 years ago

6 0

we are given

$f(x)=x^2-4x+5$

Since, we have to find inverse of this function

step-1: we set f(x)=y

$y=x^2-4x+5$

step-2: switch x and y

$x=y^2-4y+5$

step-3: Solve for y

$y^2-4y+(5-x)=0$

now, we can use quadratic formula

$y=\frac{4+\sqrt{4^2-4(5-x)} }{2}$

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

$f^{-1}(x)=-\sqrt{x-1}+2$ ..............Answer

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