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Question

If a relation R defined as R={(x,y):x,yR,y=f(x)}, where
f(x)={x|x|4,xQx|x|3,xQ, 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 C f(x) is many-one function
As each and every element of x has an unique image, given relation is a function.
(x,x)R, xR, R is not an equivalnce relation.

Now,
f(x)={x|x|4,xQx|x|3,xQ

f(2)=f(31/4)=0
f(x) is not one-one function.
So, f(x) is many-one function.

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