Using composite functions, we have that:
2. a. g(h(5)) = 284.
2. b. g(h(t)) = 9t² + 11t + 4.
3. a. [tex]f(g(x)) = x[/tex].
3. b. [tex]g(f(x)) = x[/tex].
What is the composite function of f(x) and g(x)?
The composite function of f(x) and g(x) is given by:
[tex](f \circ g)(x) = f(g(x))[/tex]
For item 2, the functions are:
The composite function of g(t) and h(t) is given by:
g(h(t)) = g(3t + 2) = (3t + 2)² - t = 9t² + 12t + 4 - t = 9t² + 11t + 4.
When t = 5, we have that:
g(h(5)) = 9(5)² + 11(5) + 4 = 284.
For item 3, the functions are:
- [tex]g(x) = \sqrt{x + 3}[/tex]
Hence the composite functions are:
- [tex]f(g(x)) = f(\sqrt{x + 3}) = (\sqrt{x + 3})^2 - 3 = x + 3 - 3 = x[/tex].
- [tex]g(f(x)) = g(x^2 - 3) = \sqrt{x^2 - 3 + 3} = \sqrt{x^2} = x[/tex].
More can be learned about composite functions at https://brainly.com/question/13502804
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