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Let A={xinR:x" is not a positive integer...

Let `A={xinR:x" is not a positive integer "}`define a function `f:AtoR" such that "f(x)=(2x)/(x-1)`. Then f is

A

Injective but not surjective

B

Surjective but not injective

C

Neither injective nor surjective

D

Not injective

Text Solution

Verified by Experts

The correct Answer is:
A
`f(x)=(2x)/(x-1)," "f(x)=2+(2)/(x-1)`
`"Say "f(x(1))=f(x_(2))" "rArr" "2+(2)/(x_(1)-1)=2+(2)/(x_(2)-1)" "rArr" "x_(1)=x_(2)`
f is injective.
Since f is one-one. f will NOT be able to take values corresponding to the value of x when x would be an integer. Therefore, f can't have `RR` as its range.
Injective NOT surjective.
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