How do you find the inverse of #f(x)=(7/x)-3#?

1 Answer
Feb 1, 2016

#f^-1(x)=7/(x+3#

Explanation:

Given that #f(x)=7/x-3#
We know that if #f(x)=y# then #f^-1(y)=x#

So, from the main equation, by rearranging we get
#y=7/x-3\impliesy+3=7/x\implies(y+3)/7=1/x#
#:.x=7/(y+3)#

We know what #x# is, so now you know why the answer above is right. (Just replace #y# to #x#)