Answer:
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
