Functions Question 127
Question: If R denotes the set of all real numbers then the function $ f:R\to R $ defined $ f(x)=\
[x] $ [Karnataka CET 2004]
Options:
A) One-one only
B) Onto only
C) Both one-one and onto
D) Neither one-one nor onto
Show Answer
Answer:
Correct Answer: D
Solution:
Let $ f(x_1)=f(x_2) $
$ \Rightarrow [x_1]=[x_2]\not{\Rightarrow }x_1=x_2 $ {For example, if x1=1.4, x2=1.5, then [1.4]=[1.5] =1}
$ \therefore $ f is not one-one. Also, f is not onto as its range I (set of integers) is a proper subset of its co-domain R.
BETA
