Question

If A ={a,b,c,d} and the function f={(a,b),(b,d),(c,a),(d,c)}, write $f^{-1}$.

Answer 1

By definition of inverse function, if $f\left(x\right)=y$, then $f^{-1}\left(y\right)=x$

Given that, A={a,b,c,d}
and $f=\left\{\right(a,b),(b,d),(c,a),(d,c\left)\right\}$

$\therefore f^{-1}=\left\{\right(b,a),(d,b),(a,c),(c,d\left)\right\}$