Find whether f:Z - Z defined by f(x) = x2 + 5 for all x belongs Z is one one or not.

the given function is f:ZZ ; f(x)=x2+5 
and f(-x)=(-x)2+5=x2+5
therefore f(x)=f(-x)
i.e. f(1)=f(-1)f(2)=f(-2)......f(k)=f(-k) ; kZ
therefore the function has same value for positive and negative x  thus function is not one-one.

hope this helps you.

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no it is not a one one function

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