Which of the following is always true for an invertible function and its inverse ?

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Which of the following is always true for an invertible function

f:X\to Y

and its inverse

f^{-1}

? (a)

f^{-1}(f(x))=x \text{ for all } x\in Y

(b)

f(f^{-1}(y))=y \text{ for all } y\in Y \text{ and } \operatorname{Dom}(f^{-1})=Y

(c)

\operatorname{Dom}(f^{-1})=X \text{ and } \operatorname{Ran}(f^{-1})=Y

(d)

f^{-1}(y)=\dfrac{1}{f(y)}