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The equations were not given in the question.
So, take random examples for the functions f(x) and g(x) to simplify.
f(g(x)) denotes the composition function.
Important note:
After computing the composition function we must define the domain of the new function.
Example 1:
f(x) = x² and g(x) = x + 4, here the domain of f and g is the set of all real numbers.
⇒ f(g(x)) = f(x + 4) = (x + 4)²
⇒ f(g(x)) = x² + 8x + 16
This new function is also defined for all the real numbers.
Example 2:
f(x) = 5/x and g(x) = x² - 4, here the domain of g is the set of all real numbers and the domain of f is the set of all real numbers except x=0.
⇒ f(g(x)) = f(x² - 4)
⇒ f(g(x)) = 5/(x² - 4) = 5/((x - 2)(x + 2))
The domain for the new function is the set of all real numbers except x=2 and x=-2.
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