5 The functions f and g are defined with their respective domains by $$\begin{array} { l l } \mathrm { f } ( x ) = x ^ { 2 } & \text { for all real values of } x
\mathrm {~g} ( x ) = \frac { 1 } { 2 x + 1 } & \text { for real values of } x , \quad x \neq - 0.5 \end{array}$$

1. Explain why f does not have an inverse.
2. The inverse of g is \(\mathrm { g } ^ { - 1 }\). Find \(\mathrm { g } ^ { - 1 } ( x )\).
3. State the range of \(\mathrm { g } ^ { - 1 }\).
4. Solve the equation \(\mathrm { fg } ( x ) = \mathrm { g } ( x )\).