Given the function FX = logax + B / X-B, find the inverse function

Given the function FX = logax + B / X-B, find the inverse function

It seems that f (x) = loga (x + b) / (X-B), right?
Let y = loga (x + b) / (X-B)
Then (x + b) / (X-B) = a ^ y
x+b=xa^y-ba^y
X = B (1 + A ^ y) / (a ^ Y-1)
So the inverse function is y = B (1 + A ^ x) / (a ^ x-1)