8. If \( f(x)=\frac{2}{x^{3}+2} \), what is \( f(1) \) ? What is \( f\left(y^{2}\right) \) ? \( f(1)=\frac{2}{3} \) (Type an integer or a simplified fraction.) \( f\left(y^{2}\right)=\frac{2}{y^{2}+2} \)

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

Resolve into partial fractions: a) \( \frac{5 x+2}{3 \mathbf{x}^{2}+4 x-4} \)

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.

The function g is such that \( \mathrm{g}(x)=2-3 x^{4} \) where \( x \neq 0 \) The function h is such that \( \mathrm{h}(x)=\frac{3 x}{2-x} \) where \( x \neq 2 \) (b) (i) Find \( \mathrm{g}(-2) \) (ii) Express the composite function hg in the form \( \mathrm{hg}(x)=\ldots \) Give your answer in its simplest form.