MHB Find Inverse of f(x) = ln(x-1)

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To find the inverse of the function f(x) = ln(x-1) for x > 1, set y = f(x). This leads to the equation y = ln(x-1), which can be rewritten as e^y = x - 1. Solving for x gives x = e^y + 1. Therefore, the inverse function is f^(-1)(y) = e^y + 1.
spartas
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find the inverse function of
f(x)=ln(x-1), x>1
 
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spartas said:
find the inverse function of
f(x)=ln(x-1), x>1

You set $y=f(x)$. Then $y= \ln (x-1) \Rightarrow e^y=x-1 \Rightarrow x=e^y+1$.

What can we deduce from that?
 

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