Functions Question 4
Question: Let $ f:R\to R $ be a function defined by $ f(x)=\frac{x-m}{x-n} $ , where $ m\ne n $ . Then
[UPSEAT 2001]
Options:
A) f is one-one onto
B) f is one-one into
C) f is many one onto
D) f is many one into
Show Answer
Answer:
Correct Answer: B
Solution:
For any $ x,,y\in R, $ we have $ f(x)=f(y)\Rightarrow \frac{x-m}{x-n}=\frac{y-m}{y-n}\Rightarrow x=y $ \ f is one-one. Let aÎR such that $ f(x)=\alpha \Rightarrow \frac{x-m}{x-n}=\alpha $ Þ $ x=\frac{m-n\alpha }{1-\alpha } $ Clearly $ x\notin R $ for $ \alpha =1 $ . So, f is not onto.
BETA
