help with inverse functions

Welllllll....that is not how the question showed up in my browser!  LOL    Thanx   Chris!

f(x) = 3x -3

y = 3x-3

x = 3y-3

x+3 = 3y

(x+3) / 3 = f'(x)

f(x)=3^x-1- 2   for f(x), write  y

y = 3^x-1- 2    add 2  to each side

y  + 2  =  3^x-1    log each side

log ( y  + 2 )  = log 3^x-1    and we can write

log ( y  + 2 )  = (x -1) log 3        divide by log 3

log ( y  + 2 ) / log 3  = x -1     add 1  to each side

[ log ( y  + 2 ) / log 3]+ 1  =  x      swap  x, y

[ log ( x + 2 ) / log 3]+ 1  =   y       for  y, write  f ^-1(x)

[ log ( x + 2 ) / log 3]+ 1  =  f ^-1(x)

See the graphs, here : https://www.desmos.com/calculator/fn6piswi4a

No prob, EP....you just answered what you saw.....LOL!!!!!!!