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

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

##### 1 Answer

Feb 14, 2017

#### Answer:

#### Explanation:

Let:

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

and solve for

First add

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

Add

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

So the inverse function can be written as:

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