For which $x$-values does a function equal its inverse?

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

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 \[ x^2+x-1=0.\]