Functions Revision Worksheet Q1

The function \({\mathrm{f}}\) is defined by

\({\mathrm{f}\left( x \right)=2+\sqrt{x}}\), \({x\in \mathbb{R}}\), \({x\ge 0}\).

1. Evaluate \({\mathrm{ff}\left( 49 \right)}\).
2. Find an expression for the inverse function, \({{{\mathrm{f}}^{-1}}\left( x \right)}\).
3. Sketch in the same set of axes of the graph of \({\mathrm{f}\left( x \right)}\) and the graph of \({{{\mathrm{f}}^{-1}}\left( x \right)}\), clearly marking the line of reflection between the two graphs.
4. Show that \({x=4}\) is the only solution of the equation \({\mathrm{f}\left( x \right)={{\mathrm{f}}^{-1}}\left( x \right)}\).