Question

If \(f:A\to B\) and \(g:B\to C\) are both bijections, which statement is the Reversal Law of Inverses?

Options

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

• \((g\circ f)^{-1}=g\circ f\)

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

• \((g\circ f)^{-1}=f\circ g\)

Answer 1

The composition \(g\circ f\) is also a bijection. Its inverse is obtained by reversing the order of the component inverses, giving \((g\circ f)^{-1}=f^{-1}\circ g^{-1}\).