How do you find the inverse function of #y=2-x#?

1 Answer
Lovecraft
Oct 2, 2015

#f(y) = 2 - y# or #x = 2 -y# or #f^(-1)(x) = 2 - x#
(They're the same thing, it's just a notational difference)

Explanation:

To find the inverse of any function, first isolate #x#

#y = 2 -x#
#y - 2 = -x#
#2 - y = x#

Replace #x# for #f(y)#

#f(y) = x = 2 - y#

Commonly though, inverse functions are represented in the form of #f^(-1)(x)#, so replace #y# for #x#

#f^(-1)(x) = 2 - x#

I personally think it muddles the point, since the function isn't taking #x# as an argument but that's the convention, so it's important to keep it in mind.

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