Question

Which equation expresses that applying a function and then its inverse returns the original input?

Options

• \(f(f^{-1}(x))=f(x)\) and \(f^{-1}(f(x))=f^{-1}(x)\)

• \(f(f^{-1}(x))=x\) and \(f^{-1}(f(x))=x\)

• \(f(f^{-1}(x))=0\) and \(f^{-1}(f(x))=0\)

• \(f(f^{-1}(x))=x^2\) and \(f^{-1}(f(x))=x^2\)

Answer 1

An inverse undoes the effect of the original function. Consequently, both compositions return the original input: \(f(f^{-1}(x))=x\) and \(f^{-1}(f(x))=x\).