If f : {5, 6} → {2, 3} and g : {2, 3} → {5, 6} are given by f = {(5, 2), (6, 3)} and g = {(2, 5), (3, 6)}, then find fog.

Question:

If $f:\{5,6\} \rightarrow\{2,3\}$ and $g:\{2,3\} \rightarrow\{5,6\}$ are given by $f=\{(5,2),(6,3)\}$ and $g=\{(2,5),(3,6)\}$, then find fog. [NCERT EXEMPLAR] [NCE

Solution:

We have,

$f:\{5,6\} \rightarrow\{2,3\}$ and $g:\{2,3\} \rightarrow\{5,6\}$ are given by $f=\{(5,2),(6,3)\}$ and $g=\{(2,5),(3,6)\}$

As,
fog(2) = f(g(2)) = f(5) = 2,
fog(3) = f(g(3)) = f(6) = 3,

So,

fog : $\{2,3\} \rightarrow\{2,3\}$ is defined as

$f \circ g=\{(2,2),(3,3)\}$

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