Question

If $f:A\to B$ is a bijective function then $f^{-1}\circ f=$

• A. $f\circ f^{-1}$
• B. $f$
• C. $f^{-1}$
• D. $I_A$ (Identity map of the set A)

Answer 1

The correct option is D $I_A$ (Identity map of the set A)

If $f:A\mapsto B$ is a bijective function and $f^{-1}:B\mapsto A$ is inverse of $f$, then $f\circ f^{-1}=I_B$ and $f^{-1}\circ f=I_A$, where $I_A$ and $I_B$ are identity functions on the set $A$ and $B$ respectively.
Hence, $f^{-1}of=I_A$.