4 The function f is defined as follows:
$$\mathrm { f } ( x ) = \sqrt { x } - 1 \text { for } x > 1$$
- Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\).
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The diagram shows the graph of \(\mathrm { y } = \mathrm { g } ( \mathrm { x } )\) where \(\mathrm { g } ( x ) = \frac { 1 } { x ^ { 2 } + 2 }\) for \(x \in \mathbb { R }\). - State the range of \(g\) and explain whether \(g ^ { - 1 }\) exists.
The function h is defined by \(\mathrm { h } ( x ) = \frac { 1 } { x ^ { 2 } + 2 }\) for \(x \geqslant 0\). - Solve the equation \(\mathrm { hf } ( x ) = \mathrm { f } \left( \frac { 25 } { 16 } \right)\). Give your answer in the form \(\mathrm { a } + \mathrm { b } \sqrt { \mathrm { c } }\), where \(a , b\) and \(c\) are
integers. integers.