Answer:
fg(x) = 3x² + 1
Step-by-step explanation:
fg(x)
f(3x² - 1)
(3x² - 1) + 2
3x² + 1
The value of the required function is [tex](3x^{3} + 6x^{2} - x - 2)[/tex].
A function represents the relation between two sets. The first one is called domain and the second one is called range.
Two given functions are:
[tex]f(x) = x + 2 \\g(x) = 3x^{2} - 1[/tex]
Therefore the required function,
[tex](fg)(x)= f(x)g(x) \\= (3x^{2} - 1)(x + 2)\\= 3x^{3} - x + 6x^{2} - 2\\ = 3x^{3} + 6x^{2} - x - 2[/tex]
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