Question

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

Answer 1

ANSWER

$( - \infty , - 7) \cup( - 7 , 0) \cup(0 , 7 )\cup(7 , + \infty )$

EXPLANATION

The given function is

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

This function is defined for values where the denominator is not equal to zero.

$x( {x}^{2} - 49) \ne0$

$x(x - 7)(x + 7) = 0$

The domain is

$x \ne - 7, x \ne0, \: and \: x \ne 7,$

Or

$( - \infty , - 7) \cup( - 7 , 0) \cup(0 , 7 )\cup(7 , + \infty )$