Question Number 26681 by Tanveer48 last updated on 28/Dec/17
$${f}:{R}×{R}\rightarrow{R}\:{such}\:{that}\:{f}\left({x}+{iy}\right)=\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} .} \\ $$$${Then}\:{f}\:{is} \\ $$$$\left.{a}\right)\:{many}−{one}\:{and}\:{into}\:{function} \\ $$$$\left.{b}\right)\:{one}−{one}\:{and}\:{onto}\:{function} \\ $$$$\left.{c}\right)\:{many}−{one}\:{and}\:{onto}\:{function} \\ $$$$\left.{d}\right)\:{one}−{one}\:{and}\:{into}\:{function} \\ $$
Commented by prakash jain last updated on 28/Dec/17
$${many}−{one}\:{as}\:\left(\mathrm{2},\mathrm{3}\right)\:{and}\:\left(\mathrm{3},\mathrm{2}\right)\:{map} \\ $$$$\:\:\:\:\:{to}\:{same}\:{value} \\ $$$${into}\:{as}\:{no}\:{pair}\:{of}\:\left({x},{y}\right)\:{will}\:{map} \\ $$$$\:\:\:\:{to}\:−{ve}\:{values}. \\ $$