Which of the following statements is always true for a bijective function with inverse ?

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

Problem

Which of the following statements is always true for a bijective function f:A→Bf:A\to B with inverse f−1f^{-1}? (a) f∘f−1=IAf\circ f^{-1}=I_A (b) f−1(a)=1f(a)  for all a∈Af^{-1}(a)=\dfrac{1}{f(a)}\;\text{for all }a\in A (c) f−1∘f=IAf^{-1}\circ f=I_A (d) f−1∘f=IBf^{-1}\circ f=I_B

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