Stating a suitable domain (composite functions) One of the questions was:

Given $f(x)=\frac{1}{x^2-4}$    &amp;    $g(x)=\frac{1}{x} -2$

a) find $g(f(x))$ (Which i think is $\frac{1}{2}$?)

b) State a suitable domain

I dont know how to write about domains - any help would be appreciated
To compute $g(f(x))$ (let's call it $h(x)$) you take

$$
y = \frac{1}{x^2-4}
$$

and replace that on $g$, yelding 

$$
g(y) = \frac{1}{\frac{1}{x^2-4}} - 2 = x^2 - 4 -2 = x^2 - 6
$$

As for the domain, this new function $h$ is defined for all $x \in \mathbb{R}$.
To compute $g(f(x))$ (let's call it $h(x)$) you take

$$
y = \frac{1}{x^2-4}
$$

and replace that on $g$, yelding 

$$
g(y) = \frac{1}{\frac{1}{x^2-4}} - 2 = x^2 - 4 -2 = x^2 - 6
$$

As for the domain, this new function $h$ is defined for all $x \in \mathbb{R}$.