(a) State the condition under which a function is said to be invertible. (b) Let and…

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

(a) State the condition under which a function is said to be invertible. (b) Let

f:A\to B

and

g:B\to C

be bijective functions. Prove that the inverse of their composition satisfies

(g\circ f)^{-1}=f^{-1}\circ g^{-1}.

(g\circ f)^{-1}

in terms of

A,B

and

C

, and explain how these sets interchange when an inverse is taken.