\begin{tabular}{|r|l} 12. \( f(x)=\frac{1}{x-3} \) \\ \( x \) & \( y \) \\ \hline-3 & \\ -2 & \\ -1 & \\ 0 & \\ 1 & \\ 2 & \\ 3 & \end{tabular}

c) \( \quad \frac{-x}{2}\left(\frac{x}{2}+3 y\right)\left(\frac{x}{2}-3 y\right) \)

3. The function f is such that \( \mathrm{f}(x)=\frac{k}{x} \) where \( x \neq 0 \) and \( k \) is an integer. (a) Express the inverse function \( \mathrm{f}^{-1} \) in the form \( \mathrm{f}^{-1}(x)=\ldots \)

(3) Determine the domain for which the functions \( f(x)=2 \mathrm{x}^{2}-1 \) and \( g(x)=1-3 x \) are equal. Solution:

لف) عبارت جبرى زير را ساده كنيد.

2. \( \mathrm{f}(x)=x^{2}-4 \) \( \mathrm{~g}(x)=2 x+1 \) Solve \( \quad \mathrm{fg}(x)>0 \) Show clear algebraic working.