Find whether **f:Z** **- Z **defined by f(x) = x^{2} + 5 for all x belongs Z is one one or not.

and $f(-x)=(-x{)}^{2}+5={x}^{2}+5$

therefore $f\left(x\right)=f(-x)$

$i.e.f\left(1\right)=f(-1)\phantom{\rule{0ex}{0ex}}f\left(2\right)=f(-2)\phantom{\rule{0ex}{0ex}}...\phantom{\rule{0ex}{0ex}}...\phantom{\rule{0ex}{0ex}}f\left(k\right)=f(-k);k\in Z$

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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