How do you find the inverse of #f(x) = x^2 +x#?

1 Answer
Edric Y.
Nov 12, 2015

#f^-1(x)=-1/2+-sqrt(x+1/4)#

Explanation:

To find an inverse, switch x and y (or f(x)).

For simplicity I will rewrite f(x) as y...
#y=x^2+x#
switch...
#x=y^2+y#
now solve for y
It looks like we need to complete the square...
#x+1/4=y^2+y+1/4#
#x+1/4=(y+1/2)^2#
#+-sqrt(x+1/4)=y+1/2# Don't forget the #+-#!
#-1/2+-sqrt(x+1/4)=y# Don't forget the #+-#!

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