- The functions f and g are defined by
$$\begin{array} { l l }
\mathrm { f } : x \mapsto 2 | x | + 3 , & x \in \mathbb { R } ,
\mathrm {~g} : x \mapsto 3 - 4 x , & x \in \mathbb { R }
\end{array}$$
- State the range of f.
- Find \(\mathrm { fg } ( 1 )\).
- Find \(\mathrm { g } ^ { - 1 }\), the inverse function of g .
- Solve the equation
$$\operatorname { gg } ( x ) + [ \mathrm { g } ( x ) ] ^ { 2 } = 0$$