How to find the equation of the inverse function (the one below)?

Question

#f(x)= 1/(-1/3(x-3))-4#

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Answer 1 · 2017-02-14T00:12:30

#f^(-1)(y) = 3-3/(y+4)#

Let:

#y = f(x) = 1/(-1/3(x-3))-4#

and solve for #x# in terms of #y#.

First add #4# to both ends to get:

#y+4 = 1/(-1/3(x-3))#

Take the reciprocal of both sides of the equation to get:

#1/(y+4) = -1/3(x-3)#

Multiply both sides by #-3# to get:

#-3/(y+4) = x-3#

Add #3# to both sides and transpose to get:

#x = 3-3/(y+4)#

So the inverse function can be written as:

#f^(-1)(y) = 3-3/(y+4)#