The function $\mathrm{f}$ is defined by $\mathrm{f}\left( x \right)=1+\sqrt{x}$, $x\in \mathbb{R}$,

Question

The function $\mathrm{f}$ is defined by $\mathrm{f}\left( x \right)=1+\sqrt{x}$, $x\in \mathbb{R}$, $x\ge 0$. Evaluate $\mathrm{ff}\left( 9 \right)$. Find an expression for the inverse function ${{\mathrm{f}}^{-1}}\left( x \right)$. Sketch in the same diagram 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. Show that $x=\frac{3+\sqrt{5}}{2}$ is the only solution of the equation $\mathrm{f}\left( x \right)={{\mathrm{f}}^{-1}}\left( x \right)$.

Accepted Answer

(a) $3$ (b) $f^{-1}(x) = (x-1)^2$, $x \geq 1$ (d) $x = \frac{3+\sqrt{5}}{2}$

J2 A Level Revision Set: Functions Q1

J2 A Level Revision Set: Functions Q1

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