Question

If $f:A\to B$ is a bijection then $f^{-1}of=$

• A. $fo{f}^{-1}$
• B. $f$
• C. $f^{-1}$
• D. an identity

Answer 1

The correct option is D an identity

Since $f$ is bijective, its inverse will also be bijective.
$f\left(x\right)=y$
$x=f^{-1}\left(y\right)$
$f\left(x\right)=f^{-1}\left(y\right)$
$y=f\left(f{)}^{-1}\right(y)=f(x)=y$
Hence, it is an identity.