If a relation R defined as R={(x,y):x,y∈R,y=f(x)}, where f(x)={x|x|−4,x∈Qx|x|−√3,x∉Q, then which among the following options is correct?
A
Relation R is not a function.
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B
f(x) is one-one function
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C
f(x) is many-one function
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D
R is an equivalance relation
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Solution
The correct option is Cf(x) is many-one function As each and every element of x has an unique image, given relation is a function. ∵(x,x)∉R,∀x∈R,R is not an equivalnce relation.
Now, f(x)={x|x|−4,x∈Qx|x|−√3,x∉Q
∵f(2)=f(31/4)=0 ⇒f(x) is not one-one function.
So, f(x) is many-one function.