If f(x)=3 x and g(x)= 1/x , what is the domain of (g o f)(x)?

The domain is (-∞ , 0)∪(0 , ∞) OR The domain is {x : x ≠ 0}

Step-by-step explanation:

* Lets revise the composite function

- A composite function is a function that depends on another function.

- A composite function is created when one function is substituted into

 another function.

- Ex: f(g(x)) is the composite function that is formed when g(x) is

 substituted for x in f(x).

- In the composition (f ο g)(x), the domain of f becomes g(x).

* Lets solve the problem

∵ f(x) = 3x and g(x) = 1/x

- In (g o f)(x) we will substitute x in g by f

∴ (g o f)(x) = 1/3x

- The domain of the function is all real values of x which make the

  function defined

- In the rational function r(x) = p(x)/q(x) the domain is all real numbers

 except the values of x which make q(x) =0

∵ (g o f)(x) = 1/3x

∵ 3x = 0 ⇒ divide both side by 3

∴ x = 0

∴ The domain of (g o f)(x) is all real numbers except x = 0

∴ The domain is (-∞ , 0)∪(0 , ∞) OR The domain is {x : x ≠ 0}