The composite functions for this problem are given as follows:
10. [tex](g \circ f)(x) = \frac{x + 4}{\sqrt{x + 1}}[/tex]
11. (f ∘ g)(x) = x + 7, domain [-5, ∞).
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 item 10, the functions are given as follows:
- [tex]f(x) = \sqrt{x + 1}[/tex].
- [tex]g(x) = \frac{x^2 + 3}{x}[/tex]
Hence the composite function is:
[tex](g \circ f)(x) = g(f(x)) = g(\sqrt{x + 1}) = \frac{(\sqrt{x + 1})^2 + 3}{\sqrt{x + 1}} = \frac{x + 4}{\sqrt{x + 1}}[/tex]
For item 11, the functions are given as follows:
- [tex]f(x) = x^2 + 2[/tex].
- [tex]g(x) = \sqrt{x + 5}[/tex]
Hence the composite function is:
[tex](f \circ g)(x) = f(g(x)) = f(\sqrt{x + 5}) = (\sqrt{x + 5})^2 + 2 = x + 5 + 2 = x + 7[/tex]
There is a restriction in the domain of g(x), as the term inside the root cannot be negative, and this restriction is considered for the composite function, hence the domain is:
[-5, ∞).
Hence:
(f ∘ g)(x) = x + 7, domain [-5, ∞).
More can be learned about composite functions at https://brainly.com/question/13502804
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