How do you find the inverse of #y=2(3)^x +1#?

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Answer 1 · 2015-11-25T09:54:15

To find the inverse function you have to transform the formula #y=f(x)# to #x=f(y)#. For this example see explanation:

You have a function:

#y=2*(3^x)+1#

Now we are trying to calculate #x#:

#y-1=2*3^x#

#(y-1)/2=3^x#

#x=log_3 ((y-1)/2)#

Answer: The inverse function is: #f(x)=log_3((x-1)/2)#

Note: In the answer you usualy write the inverse function as: #y=f(x)#.