A function \(f\) is defined by \(f:x\rightarrow \dfrac{1}{x+1}\). Write down in similar form expressions for \(f^{-1}...\)

How can we find the inverse function? What happens if we make \(x\) the subject of \(y=f(x)\)?

… and \(ff\).

Would it help to view the composite function \(ff(x)\) as \(f(f(x))\)?

It is required to find the values of \(x\) for which \((i)\) \(f=f^{-1}\), \((ii)\) \(f=ff\).

Show that, in each case, the values of \(x\) are given by the equation \[x^2+x-1=0.\]

From the above, we should now know \(f(x)\), \(f^{-1}(x)\) and \(ff(x)\). Can we form equations using these?