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Question

Show that the function f:RR defined by f(x)=xx2+1 xR is neither one-one nor onto.

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Solution

put xa,x=b
let f(a)=f(b)
aa2+1=bb2+1
ab2+a=ba2+b
ab(ba)=ba
ab=0
so f(x) is not one one function
now f(x)=xx2+1=y
x value cannot be found that is f1(x) does not exist so f(x) is not onto function

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