Question

determine where the function m(x)=\frac{x + 4}{(x - 4)(x - 7)} is continuous.
the function is continuous on .
(simplify your answer. type your answer in interval notation.)

Explanation:

Step1: Identify points of discontinuity

A rational function is discontinuous where the denominator is 0. Set $(x - 4)(x - 7)=0$.
$(x - 4)(x - 7)=0$ implies $x-4 = 0$ or $x - 7=0$, so $x = 4$ and $x=7$.

Step2: Write the intervals of continuity

The function is continuous on the intervals that do not include these points of discontinuity. In interval - notation, the function is continuous on $(-\infty,4)\cup(4,7)\cup(7,\infty)$.

Answer:

$(-\infty,4)\cup(4,7)\cup(7,\infty)$