Find inverse for function: f(x)=2(3^x-1)-5

Question

basic concept 

Answer 1

To find the inverse function you need 2 steps.

1:  swap all x's and y's

2:  solve for y.  this will be the inverse function.

 

 

Step 1:  original was y = 2(3^x-1)-5     so replace every y with an x.  replace every x with a y.

 

      x = 2(3^y-1)-5

 

Step 2:  now solve for y.

 

       x + 5 = 2(3^y-1)

 

      (x + 5)/2 = 3^y - 1

 

     (x + 5)/2 + 1 = 3^y

 

log₃[(x+5)/2 + 1] = y = the inverse function.

 

 

If the problem was   f(x) = 2(3^x-1) - 5, then the answer will be different.  Is the exponent just "x" or is it "x-1"?