Question

determine where the following function is continuous.
m(x)=\frac{x - 5}{4x^{2}-9}
the function is continuous on
(type your answer in interval notation. use integers or fractions for any numbers)

Explanation:

Step1: Find denominator - zero points

Set $4x^{2}-9 = 0$. Then $4x^{2}=9$, so $x^{2}=\frac{9}{4}$, and $x=\pm\frac{3}{2}$.

Step2: Determine continuity intervals

A rational - function is continuous everywhere except where the denominator is zero. So the function $M(x)=\frac{x - 5}{4x^{2}-9}$ is continuous on $(-\infty,-\frac{3}{2})\cup(-\frac{3}{2},\frac{3}{2})\cup(\frac{3}{2},\infty)$.

Answer:

$(-\infty,-\frac{3}{2})\cup(-\frac{3}{2},\frac{3}{2})\cup(\frac{3}{2},\infty)$