Answer :
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Step-by-step explanation:
The function f(g(x)) is an illustration of a composite function of f(x) and g(x). The composite function f(g(x)) is [tex]f(g(x)) = 18x^3 + 1[/tex]
Given that:
[tex]f(x) = 9x^2 + 1[/tex]
[tex]g(x) = \sqrt{2x^3}[/tex]
f(g(x)) is calculated as follows:
[tex]f(x) = 9x^2 + 1[/tex]
Substitute g(x) for x
[tex]f(g(x)) = 9(g(x)^2) + 1[/tex]
Substitute [tex]g(x) = \sqrt{2x^3}[/tex]
[tex]f(g(x)) = 9((\sqrt{2x^3})^2) + 1[/tex]
[tex]f(g(x)) = 9(2x^3) + 1[/tex]
Open bracket
[tex]f(g(x)) = 18x^3 + 1[/tex]
Hence, composite function f(g(x)) is [tex]f(g(x)) = 18x^3 + 1[/tex]
Read more about composite functions at:
https://brainly.com/question/8776301