Functions - Inverse Functions

• For \({\mathrm{f}^{-1}}\) to exist, \({\mathrm{f}}\) must be a one-one function.
• \({\mathrm{f}}\) is the reflection of \({\mathrm{f}^{-1}}\) in the line \({y = x}\).
• \({D_{\mathrm{f}^{-1}} = R_{\mathrm{f}}}\)
• \({R_{\mathrm{f}^{-1}} = D_{\mathrm{f}}}\)
• Point \({A(r, p)}\) on \({\mathrm{f}}\) will correspond to \({A'(p, r)}\) on \({\mathrm{f}^{-1}}\).
• To find \({\mathrm{f}(x) = \mathrm{f}^{-1}(x)}\) implies \({\mathrm{f}(x) = \mathrm{f}^{-1}(x) = x}\) as \({y = \mathrm{f}(x)}\), \({y = \mathrm{f}^{-1}(x)}\) and \({y = x}\) meet at the point(s) of intersections.