5 The functions f and g are defined with their respective domains by
$$\begin{array} { l l }
\mathrm { f } ( x ) = \sqrt { 2 x - 5 } , & \text { for } x \geqslant 2.5
\mathrm {~g} ( x ) = \frac { 10 } { x } , & \text { for real values of } x , \quad x \neq 0
\end{array}$$
- State the range of f .
- Find \(\mathrm { fg } ( x )\).
- Solve the equation \(\operatorname { fg } ( x ) = 5\).
- The inverse of f is \(\mathrm { f } ^ { - 1 }\).
- Find \(\mathrm { f } ^ { - 1 } ( x )\).
- Solve the equation \(\mathrm { f } ^ { - 1 } ( x ) = 7\).