Explain direct and inverse image.

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$$\begin{gathered} \mathrm{First} \mathrm{of} \mathrm{all} \\ \mathrm{f}:\mathrm{A}\to \mathrm{B} \mathrm{means} \mathrm{A}\hspace{0.17em}\mathrm{is} \mathrm{domain} \mathrm{of} \mathrm{function} \mathrm{and} \mathrm{B} \mathrm{is} \mathrm{called} \mathrm{co}-\mathrm{domain} \mathrm{of} \\ \mathrm{function}. \\ \mathrm{Also} \mathrm{range} \mathrm{of} \mathrm{function} \mathrm{is} \mathrm{always} \mathrm{subset} \mathrm{of} \mathrm{co}-\mathrm{domain}. \\ \mathrm{Suppose} \\ \mathrm{f}:\left\{1,2,3\right\}\to \left\{0,1,2,3,4,5,6,7,8,9\right\} \mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^2 \\ \mathrm{Now} \\ \mathrm{f}\left(1\right)=1^2=1 \\ \mathrm{f}\left(2\right)=2^2=4 \\ \mathrm{f}\left(3\right)=3^2=9 \\ \mathrm{Hence} \mathrm{range} \mathrm{is} \left\{1,4,9\right\} \mathrm{which} \mathrm{is} \mathrm{called} \mathrm{direct} \mathrm{image} \mathrm{of} \mathrm{set} \left\{1,2,3\right\} \\ \mathrm{under} \mathrm{the} \mathrm{given} \mathrm{function} \mathrm{f}\left(\mathrm{x}\right) \\ \mathrm{Similarly} \left\{1,2,3\right\} \mathrm{is} \mathrm{called} \mathrm{inverse} \mathrm{image} \mathrm{ofset} \left\{1,4,9\right\} \mathrm{under} \mathrm{the} \\ \mathrm{given} \mathrm{fucntion} {\mathrm{f}}^{-1} \end{gathered}$$

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