The domain and the composite function of f(x) and g(x) is given as follows:
- Composite function: [tex](f \circ g)(x) = -\frac{7}{\sqrt{x + 3}}[/tex]
What is the composite function of f(x) and g(x)?
The composite function of f(x) and g(x) is given by:
(f ∘ g)(x) = f(g(x)).
For this problem, the functions are given as follows:
- [tex]f(x) = -\frac{7}{x}[/tex]
- [tex]g(x) = \sqrt{x + 3}[/tex].
The composite function is:
[tex](f \circ g)(x) = f(\sqrt{x + 3}) = -\frac{7}{\sqrt{x + 3}}[/tex]
For a fraction, the denominator cannot be zero, and the square root only exists for non-negative numbers hence the domain is given by:
x > -3.
More can be learned about composite functions at https://brainly.com/question/13502804
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