8 Functions f and g are defined for \(0 \leqslant x \leqslant 2 \pi\) by \(\mathrm { f } ( x ) = 2 \tan x\) and \(\mathrm { g } ( x ) = \sec x\).
- State the range of f .
- State the range of \(g\).
- Show that \(\operatorname { fg } ( 0.6 ) = 5.33\), correct to 3 significant figures.
- Explain why \(\mathrm { f } ^ { - 1 } \mathrm {~g} ( 0.6 )\) is not defined.
- In this question you must show detailed reasoning.
Solve the equation \(( \mathrm { f } ( x ) ) ^ { 2 } + 6 \mathrm {~g} ( x ) = 0\).