Functions Question 201
Question: If $ f(x)=\frac{2x-1}{x+5} $ $ (x\ne -5) $ , then $ {f^{-1}}(x) $ is equal to
[MP PET 2004]
Options:
A) $ \frac{x+5}{2x-1},\ x\ne \frac{1}{2} $
B) $ \frac{5x+1}{2-x},\ x\ne 2 $
C) $ \frac{5x-1}{2-x},\ x\ne 2 $
D) $ \frac{x-5}{2x+1},\ x\ne \frac{1}{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ f(x)=y $
Þ $ x={f^{-1}}(y) $ . Now, $ y=\frac{2x-1}{x+5},(x\ne -5) $ $ xy+5y=2x-1\Rightarrow 5y+1=2x-xy $ .
Þ $ x(2-y)=5y+1\Rightarrow x=\frac{5y+1}{2-y} $
Þ $ {f^{-1}}(y)=\frac{5y+1}{2-y} $ \ $ {f^{-1}}(x)=\frac{5x+1}{2-x},x\ne 2 $ .
BETA
