1. Tardigrade
  2. Question
  3. Mathematics
  4. Let the function f be defined by f(x)=(2x+1/1-3x) Then f-1(x) is:

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Let the function $ f $ be defined by $ f(x)=\frac{2x+1}{1-3x} $ Then $ {{f}^{-1}}(x) $ is:

KEAMKEAM 2002

Solution:

Let $ y=\frac{2x+1}{1-3x} $ $ \Rightarrow $ $ y-3xy=2x+1 $ $ \Rightarrow $ $ y-1=(3y+2)x $ $ \Rightarrow $ $ x=\left( \frac{y-1}{3y+2} \right) $ $ \therefore $ $ {{f}^{-1}}(y)=\frac{y-1}{3y+2} $ $ \Rightarrow $ $ {{f}^{-1}}(x)=\frac{x-1}{3x+2} $