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Question
If the mapping f : {1, 3, 4} → {1, 2, 5} and g : {1, 2, 5} → {1, 3}, given by f = {(1, 2), (3, 5), (4, 1)} and g = {(2, 3), (5, 1), (1, 3)}, then write fog. [NCERT EXEMPLAR]
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Solution
We have,
f : {1, 3, 4}
→ {1, 2, 5} and g : {1, 2, 5}
→ {1, 3}, are given by f = {(1, 2), (3, 5), (4, 1)} and g = {(2, 3), (5, 1), (1, 3)}, respectively
As,
\[fog\left( 2 \right) = f\left( g\left( 2 \right) \right) = f\left( 3 \right) = 5, \]
\[fog\left( 5 \right) = f\left( g\left( 5 \right) \right) = f\left( 1 \right) = 2, \]
\[fog\left( 1 \right) = f\left( g\left( 1 \right) \right) = f\left( 3 \right) = 5, \]
\[So, \]
\[fog : \left\{ 1, 2, 5 \right\} \to \left\{ 1, 2, 5 \right\} \text{ is given by}\]
\[fog = \left\{ \left( 2, 5 \right), \left( 5, 2 \right), \left( 1, 5 \right) \right\}\]
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