Functions Question 494
Question: If $ f:R\to R,f(x)= \begin{cases} x| x |-4,x\in Q \\ x| x |-\sqrt{3},x\notin Q \\ \end{cases}, $ then $ f(x) $ is
Options:
A) Many to one and onto
B) Many to one and one to many
C) one-to-one and into
D) one-to-one and onto
Show Answer
Answer:
Correct Answer: D
Solution:
$ f(2)=f( {3^{1/4}} )\Rightarrow $ many to one function And $ f(x)\ne -\sqrt{3}\forall x\in R\Rightarrow $ onto function
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