Question

Let $S=\{a,b,c\}$ and $T=\{1,2,3\}$. Find $F^{-1}$ of the following function F from S to T, if it exists.

$\left(i\right)F=\left\{\right(a,3),(b,2),(c,1\left)\right\}$

Answer 1

We know that A function has inverse if it is one-one and onto.
F={(a, 3),(b, 2),(c, 1)}
Since each element has unique image,
F is one-one.
Since for every image, there is a corresponding element, F is onto.
Since, function is both one-one and onto it will have inverse.
F = {(a, 3),(b, 2), (c, 1)}
$F^{-1}=(3,a),(2,b),(1,c)$