\(f(x)\)

\(f^{-1}(x)\)

When the inverse is represented graphically we see that:

• a function and its inverse are reflections of each other through the line \(y=x\).
• the domain of \(f(x)\) is the range of \(f^{-1}(x)\)
• the range of \(f(x)\) is the domain of \(f^{-1}(x)\)
• the functions \(f(x)\) and \(f^{-1}(x)\) are inverses of each other, so
  \(ff^{-1}(x)= f^{-1}f(x)=x\)