Answer only one of the following two alternatives.
EITHER
A function \(f\) is such that \(f (x)=\ln (5 x-10),\) for \(x>2\)
(i) State the range of \(f\).
(ii) Find \(f ^{-1}(x)\).
(iii) State the range of \(f ^{-1}\).
(iv) Solve \(f(x)=0\).
A function \(g\) is such that \(g (x)=2 x-\ln 2,\) for \(x \in R\).
(v) Solve \(g f(x)=f\left(x^{2}\right)\)
OR
A function \(f\) is such that \(f (x)=4 e ^{-x}+2,\) for \(x \in R\).
(i) State the range of \(f\).
(ii) Solve \(f(x)=26\).
(iii) Find \(f ^{-1}(x)\).
(iv) State the domain of \(f ^{-1}\).
A function \(g\) is such that \(g (x)=2 e ^{x}-4,\) for \(x \in R\)
(v) Using the substitution \(t= e ^{x}\) or otherwise, solve \(g (x)= f (x)\).