Let $\mathrm{A}=\{1,2,3,4,5\}$ and the functions $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{A}$ and $\mathrm{g}: \mathrm{A} \rightarrow \mathrm{A}$ be defined by $\mathrm{f}(1)=3, \mathrm{f}(2)=5, \mathrm{f}(3)=3, \mathrm{f}(4)=1, \mathrm{f}(5)=2 ; \mathrm{g}(1)=4$, $\mathrm{g}(2)=1, \mathrm{~g}(3)=1, \mathrm{~g}(4)=2, \mathrm{~g}(5)=3$. Then

Question

Let $\mathrm{A}=\{1,2,3,4,5\}$ and the functions $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{A}$ and $\mathrm{g}: \mathrm{A} \rightarrow \mathrm{A}$ be defined by $\mathrm{f}(1)=3, \mathrm{f}(2)=5, \mathrm{f}(3)=3, \mathrm{f}(4)=1, \mathrm{f}(5)=2 ; \mathrm{g}(1)=4$, $\mathrm{g}(2)=1, \mathrm{~g}(3)=1, \mathrm{~g}(4)=2, \mathrm{~g}(5)=3$. Then, $\mathrm{fog}=\{(1,1),(2,3),(3,2),(4,5)$,, $\operatorname{fog}=\{(1,1),(2,3),(3,3),(4,5),(5,3)\}$, $\mathrm{gof}=\{(1,1),(2,3),(3,3),(4,4), 5,5)$, gof $=\{(2,2),(2,3),(3,1),(4,1),(5,1)\}$

MARKS App · Accepted Answer

We have $\begin{aligned} & (\mathrm{gof})(1)=\mathrm{g}(\mathrm{f}(1))=\mathrm{g}(3)=1 \ & (\mathrm{fog})(1)=\mathrm{f}(\mathrm{g}(1))=\mathrm{f}(4)=1 \ & (\mathrm{gof})(2)=\mathrm{g}(\mathrm{f}(2))=\mathrm{g}(5)=3 \ & (\mathrm{fog})(2)=\mathrm{f}(\mathrm{g}(2))=\mathrm{f}(1)=3 \ & (\mathrm{gof})(3)=\mathrm{g}(\mathrm{f}(3))=\mathrm{g}(3)=1 \ & (\mathrm{fog})(3)=\mathrm{f}(\mathrm{g}(3))=\mathrm{f}(1)=3 \ & (\mathrm{gof})(4)=\mathrm{g}(\mathrm{f}(4))=\mathrm{g}(1)=4 \ & (\mathrm{fog})(4)=\mathrm{f}(\mathrm{g}(4))=\mathrm{f}(2)=5 \ & (\mathrm{gof})(5)=\mathrm{g}(\mathrm{f}(5))=\mathrm{g}(2)=1 \ & (\mathrm{fog})(5)=\mathrm{f}(\mathrm{g}(5))=\mathrm{f}(3)=3 \ & \therefore \mathrm{gof}=\{(1,1),(2,3),(3,1),(4,4),(5,1)\} \ & \text { and fog }=\{(1,1),(2,3),(3,3),(4,5),(5,3)\} . \end{aligned}$

Search any question & find its solution

Looking for more such questions to practice?