Question

Can you help me with domain?g(x)= (x-2)/(x^2-16)

Answer 1

The domain of a function is composed of all real numbers for which the function is defined. In the case of a rational expression, such as the given one the function is undefined when its denominator is zero.

Now, solving

`x^(2)-16=0`

for x we get:

`\begin{gathered} x^2-16=x^2-4^2=(x-4)(x+4) \\ \text{Therefore, x=4 or x=-4} \end{gathered}`

Then, the domain of the function is al real numbers except for 4 and -4.