Math  /  Algebra

QuestionEvaluate (fg)(x)(f \circ g)(x) and find its domain. Given f(x)=5x2+36f(x)=\frac{5}{x^{2}+36} and g(x)=4+xg(x)=\sqrt{4+x}.

Studdy Solution
The domain of the function (fg)(x)(f \circ g)(x) is all real numbers except 40-40. In interval notation, this is written as (,40)(40,)(-\infty, -40) \cup (-40, \infty).
So, the composite function (fg)(x)(f \circ g)(x) is 540+x\frac{5}{40+x} and its domain in interval notation is (,40)(40,)(-\infty, -40) \cup (-40, \infty).

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