Question

find the domain of g(x)= x/x^2-49.answer in interval notation

Answer 1

Explanation

Given

$g(x)=\frac{x}{x^2-49}$

The domain of the function is the set of x values that will make the function defined. This is given below.

Using the denominator, we will find the point of singularity.

$\begin{gathered} x^2-49=0 \\ x^2=49 \\ x=7,x=-7 \end{gathered}$

Therefore, the points of singularities are 7 and -7. Hence we will exclude those points from the set of real numbers.

Answer:

$(-\infty-7)\cup(-7,7)\cup(7,\infty)$