The function \(f\) from \(\mathbb{R}\) to \(\mathbb{R}\) is given by \(f: x\mapsto x^2+2x+2\). Find the range of \(f\), and state, with a reason, whether or not \(f\) is bijective.

The range of \(f\) is denoted by \(S\), and the function \(g\) from \(S\) to \(\mathbb{R}\) is given by \(g: x\mapsto 1/x\). State the image of \(x\) under the composite function \(g\circ f\), and give the range of this composite function.

\(R'\) denotes the set of real numbers excluding \(0\) and \(1\). Functions \(\phi\) and \(\psi\) from $ R’$ to \(R'\) are given by \[\phi : x\mapsto \frac{1}{1-x}, \qquad \qquad \psi : x \mapsto 1-x.\]

Give in a similar form the definitions of \(\phi ^{-1}\) and \((\phi \circ \psi)^{-1}\).