Question

H(x)= 9/x( x^2-49)
Determine the domain of the function

Answer 1

Answer: The domain of the function $h(x) = \frac{9}{x(x^2-49)}$ is:

Interval Notation: (-∞ , -7) ∪ (-7 , 0) ∪ (0 , 7) ∪ (7, ∞)

Set-Builder Notation: { x | x ≠ 0 , 7 , -7 }

All real numbers besides 0, 7, and -7.

Step-by-step explanation:

In order to find the domain of your rational function, we need to simplify it:

$h(x) = \frac{9}{x(x^2-49)} = \frac{9}{(x)(x+7)(x-7)}$

Remember, most of the time, the domain of a rational function consists of all real numbers besides zero.

To find the domain, we equal the equations in the denominator to zero.

$x=0$

$x+7=0$ --> $x=-7$

$x-7=0$ --> $x=7$

So all real numbers except for 0, -7, and 7 are in the domain of this rational function.