Math  /  Algebra

QuestionExplain how to find f(g(x))f(g(x)) from f(x)f(x) and g(x)g(x), and determine its domain in interval notation.

Studdy Solution
The domain of f(g(x))f(g(x)) is all real numbers except -40. In interval notation, this is represented as (,40)(40,)(- \infty, -40) \cup (-40, \infty).
The function f(g(x))=540+xf(g(x)) = \frac{5}{40 + x} was obtained by substituting g(x)g(x) into f(x)f(x) and simplifying. The domain of f(g(x))f(g(x)) is (,40)(40,)(- \infty, -40) \cup (-40, \infty).

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