Let f\displaystyle {f} and g\displaystyle {g} be functions defined as follows:

 f={(38,4),(39,214),(40,−138),(41,737),(42,117)}\displaystyle {f}={\left\lbrace{\left({38},{4}\right)},{\left({39},\frac{{21}}{{4}}\right)},{\left({40},-\frac{{13}}{{8}}\right)},{\left({41},\frac{{7}}{{37}}\right)},{\left({42},\frac{{1}}{{17}}\right)}\right\rbrace} 

 g={(38,−3),(39,15),(40,1623),(41,−16),(42,−358)}\displaystyle {g}={\left\lbrace{\left({38},-{3}\right)},{\left({39},{15}\right)},{\left({40},\frac{{16}}{{23}}\right)},{\left({41},-{16}\right)},{\left({42},-\frac{{35}}{{8}}\right)}\right\rbrace} 

Compute the indicated value, if it exists.

(i) (f+f)(38)=\displaystyle {\left({f}+{f}\right)}{\left({38}\right)}=   

(ii) (g−g)(41)=\displaystyle {\left({g}-{g}\right)}{\left({41}\right)}=  

(iii) (f⋅f)(40)=\displaystyle {\left({f}\cdot{f}\right)}{\left({40}\right)}=   

(iv)  (fg)(39)=\displaystyle {\left(\frac{{f}}{{g}}\right)}{\left({39}\right)}=   

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