The function f is defined by \( \mathrm{f}:x\mapsto \frac{2x+a}{x+b},\quad x\in\mathbb{R}, x\ne -b\text{ and}\hspace{0.5em}a\ne 2b,\)
where \(b\) is a real constant.
Find \(\mathrm{f}^{-1}(x)\) in terms of \(a\) and \(b\). State the domain of \(\mathrm{f}^{-1}\).[2]
The function f is such that \(\mathrm{f}(x)=\mathrm{f}^{-1}(x)\) for all \(x\) in the domain of f.
Find the possible values of \(a\) and \(b\).[2]
The function g is defined by
\(\mathrm{g}:x\mapsto 7+\sqrt{x-3},\quad x\in\mathbb{R},\ x\ge 3.\)
Using the values \(a=-1\) and \(b=1\),
Show that fg exists.[2]
Find the value of fg(7).[1]
Find the exact range of fg.[2]