# If the mapping f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3}, given by

Question:

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

[NCERT EXEMPLAR]

Solution:

We have,

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

As,

$f o g(2)=f(g(2))=f(3)=5$

$f o g(5)=f(g(5))=f(1)=2$

$f o g(1)=f(g(1))=f(3)=5$

So,

$f o g:\{1,2,5\} \rightarrow\{1,2,5\}$ is given by

$f o g=\{(2,5),(5,2),(1,5)\}$