9709 P11 - Jun 2025 - Q10 - 12 marks
9694
\[f(x)=\sqrt x\quad(x\ge0),\qquad g(x)=3\sqrt{x+2}-5\quad(x\ge-2).\]
(a) Describe fully an ordered sequence of transformations mapping \(y=f(x)\) to \(y=g(x)\). [5]
(b) On the diagram sketch \(y=g^{-1}(x)\), together with the relevant mirror line. [2]
(c) Find \(g^{-1}(x)\). [2]
(d) State the range of \(g^{-1}\). [1]
\(h(x)=x-2\) for \(x\ge0\).
(e) Find \(g^{-1}h(4)\). [1]
(f) Explain why \(hg^{-1}\) cannot be formed. [1]
