A) f is one-one onto
B) f is one-one into
C) f is many one onto
D) f is many one into
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.
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