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

1 Answer
BB
Apr 10, 2018

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)#

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