Answer:
The function domain is:
[tex]x<-6\quad \mathrm{or}\quad \:-6<x<0\quad \mathrm{or}\quad \:0<x<6\quad \mathrm{or}\quad \:x>6[/tex]
Step-by-step 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 [tex]h(x)=\frac{9x}{x(x^{2}-6^{2})}[/tex]
since, (a²-b²) =(a+b)(a-b)
[tex]h(x)=\frac{9x}{x(x-6)(x+6)}[/tex]
Find undefined singularity points x=0, x=-6, x=6
The function domain is:
[tex]x<-6\quad \mathrm{or}\quad \:-6<x<0\quad \mathrm{or}\quad \:0<x<6\quad \mathrm{or}\quad \:x>6[/tex]
