Functions Question 671
Question: Let X and Y be subsets of R, the set of all real numbers. The function $ f:X\to Y $ defined by $ f(x)=x^{2} $ for $ x\in X $ is one-one but not onto if (Here $ {R^{+}} $ is the set of all positive real numbers)
[EAMCET 2000]
Options:
A) $ X=Y={R^{+}} $
B) $ X=R,\ Y={R^{+}} $
C) $ X={R^{+}},\ Y=R $
D) $ X=Y=R $
Show Answer
Answer:
Correct Answer: C
Solution:
$ f(x_1)=f(x_2)\Rightarrow x_1^{2}=x_2^{2}\Rightarrow x_1=x_2 $ , [if $ X={R^{+}}] $
Þ f is one-one. Since $ R_{f}={R^{+}}\subseteq R=Y $ ; \ f is not onto.
BETA
