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 \(g (x)= f (x)\).