What is the inverse of the function? f(x)=3^x-1

f ^ -1 (x) =log3 (x)  +1  

Step-by-step explanation:

To find the inverse of the function, exchange x and y and solve for y

y = 3^(x-1)

Exchange x and y

x = 3^(y-1)

Solve for y

Take the log base 3 of each side

log3(x) = log(3) 3 ^ (y-1)

log3(x)  = y-1

Add 1 to each side

log3 (x)  +1 = y-1+1

log3 (x)  +1 = y

So the inverse  f ^ -1 (x) =log3 (x)  +1