Answer:
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}
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