What is the inverse of #y = log_3(x-2)# ?

1 Answer
Feb 17, 2016

Answer:

Inverse to #f(x)=log_3(x-2)# is #g(x)=3^x+2#.

Explanation:

Function #y=f(x)# is inverse to #y=g(x)# if and only if the composition of these function is an identity function #y=x#.

The function we have to inverse is #f(x)=log_3(x-2)#
Consider function #g(x)=3^x+2#.

The composition of these functions is:
#f(g(x)) = log_3(3^x+2-2) = log_3(3^x) = x#

The other composition of the same functions is
#g(f(x)) = 3^(log_3(x-2))+2 = x-2+2 = x#

As you see, inverse to #f(x)=log_3(x-2)# is #g(x)=3^x+2#.