Find Inverse of f(x) = ln(x-1)

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SUMMARY

The inverse function of f(x) = ln(x-1) for x > 1 is derived by setting y = f(x). This leads to the equation y = ln(x-1), which can be transformed into e^y = x - 1. Consequently, the inverse function is x = e^y + 1, indicating that f-1(y) = ey + 1.

PREREQUISITES
  • Understanding of logarithmic functions
  • Knowledge of exponential functions
  • Familiarity with function inverses
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the properties of logarithmic and exponential functions
  • Learn how to find inverses of other common functions
  • Explore the applications of inverse functions in calculus
  • Investigate the graphical representation of functions and their inverses
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Students studying calculus, mathematicians interested in function analysis, and educators teaching inverse functions in mathematics.

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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