Question:
Let $A=\{1,2,3,4,5,6)$ and $B=(2,4,6,8,10,12)$. If $f: A \rightarrow B$ is given by $f(x)=2 x$, then $f^{-1}$ as set of ordered pairs, is ___________.
Solution:
Given: A function f : A → B defined as f(x) = 2x, where A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6, 8, 10, 12}
Since, $f(x)=2 x$
Therefore,
$f=\{(1,2),(2,4),(3,6),(4,8),(5,10),(6,12)\}$
Hence,
$f^{-1}=\{(2,1),(4,2),(6,3),(8,4),(10,5),(12,6)\}$
Hence, if $f: A \rightarrow B$ is given by $f(x)=2 x$, then $f^{-1}$ as set of ordered pairs, is {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6)}.
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