Determine the domain of the function h(x)= 9x/x(x^2-36)

Question

asked Sep 22, 2019 161k views

2 Answers

Siviwe · Answer 1 · 2019-09-24T15:08:58+0000

Answer:

The function domain is:

$x<-6\quad \mathrm{or}\quad \:-6<x<0\quad \mathrm{or}\quad \:0<x<6\quad \mathrm{or}\quad \:x>6$

Explanation:

The domain of a function is the set of input or argument values for which the function is real and defined

Re-write the function as
h(x)=(9x)/(x(x^(2)-6^(2)))

since, (a²-b²) =(a+b)(a-b)

h(x)=(9x)/(x(x-6)(x+6))

Find undefined singularity points x=0, x=-6, x=6

The function domain is:

$x<-6\quad \mathrm{or}\quad \:-6<x<0\quad \mathrm{or}\quad \:0<x<6\quad \mathrm{or}\quad \:x>6$

Golam Moula · Answer 2 · 2019-09-27T20:39:58+0000

The function

h(x)=(9x)/(x(x^(2)-36))

is all real numbers except those that make the denominator zero.

The domain is "all real numbers except {-6, 0, +6}".