Question

If the mapping f : {1, 3, 4} $\to$ {1, 2, 5} and g : {1, 2, 5} $\to$ {1, 3}, given by f = {(1, 2), (3, 5), (4, 1)} and g = {(2, 3), (5, 1), (1, 3)}, then write fog. [NCERT EXEMPLAR]

Answer 1

We have,

f : {1, 3, 4} $\to$ {1, 2, 5} and g : {1, 2, 5} $\to$ {1, 3}, are given by f = {(1, 2), (3, 5), (4, 1)} and g = {(2, 3), (5, 1), (1, 3)}, respectively


As,

$$\begin{gathered} fog\left(2\right)=f\left(g\left(2\right)\right)=f\left(3\right)=5, \\ fog\left(5\right)=f\left(g\left(5\right)\right)=f\left(1\right)=2, \\ fog\left(1\right)=f\left(g\left(1\right)\right)=f\left(3\right)=5, \\ \mathrm{So}, \\ fog:\left\{1,2,5\right\}\to \left\{1,2,5\right\}\mathrm{is}\mathrm{given}\mathrm{by} \\ fog=\left\{\left(2,5\right),\left(5,2\right),\left(1,5\right)\right\} \end{gathered}$$