finding domain of composite function

[strugglingwithAlg]

Could someone point me in the right direction finding the domain of composite functions? I just cannot seem to grasp these types of problems.

Find the domain of the composite function, f(g(x))


\(\displaystyle f(x) = \frac{3}{{x + 6}}\) , \(\displaystyle g(x) = \frac{{30}}{x}\)

 

[Gene]

g(x) can have any x except 0
f(g(x)) =
f(30/x) =
3/((30/x)+6) so it can have any x except 0 or -5

 

[strugglingwithAlg]

would the answer be (-infinity, infinity)?

 

[Gene]

Nope, the two points 0 and -5 have to be excluded.

 

[opticaltempest]

Using interval notation to write the domain we have,


\(\displaystyle \L
( - \infty , - 5) \cup ( - 5,0) \cup (0,\infty )\)