# Function Oct/Nov 2011 Paper 13

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 $$g (x)= f (x)$$.