Functions Question 157
Question: The function $ f:R\to R $ defined by $ f(x)=(x-1) $ $ (x-2)(x-3) $ is
[Roorkee 1999]
Options:
A) One-one but not onto
B) Onto but not one-one
C) Both one-one and onto
D) Neither one-one nor onto
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ f(x)=(x-1)(x-2)(x-3) $ and $ f(1)=f(2)=f(3)=0 $
Þ $ f(x) $ is not one-one. For each x $ y\in R $ , there exists $ x\in R $ such that $ f(x)=y $ . Therefore f is onto. Hence $ f:R\to R $ is onto but not one-one.
BETA
