Question

A function \(f:X\to Y\) is defined to be invertible if there exists a function \(g:Y\to X\) such that which conditions hold?

Options

• \(g\circ f=I_Y\) and \(f\circ g=I_X\)

• \(g\circ f=0\) and \(f\circ g=0\)

• \(g\circ f=f\) and \(f\circ g=g\)

• \(g\circ f=I_X\) and \(f\circ g=I_Y\)

Answer 1

An invertible function has a function \(g:Y\to X\) that reverses the action of \(f\). The required identities are \(g\circ f=I_X\) and \(f\circ g=I_Y\), where \(I_X\) and \(I_Y\) are identity functions.