Answer:
The composite function is
[tex](f \circ g)(x) = 3x^2 + 5[/tex]
Step-by-step explanation:
Composite functions:
Suppose that we have two functions, f and g. Their composite is given by:
[tex](f \circ g)(x) = f(g(x))[/tex]
In this question:
We have that:
[tex]f(x) = 3x + 2[/tex]
[tex]g(x) = x^2 + 1[/tex]
The composite function is:
[tex](f \circ g)(x) = f(g(x)) = f(x^2+1) = 3(x^2 + 1) + 2 = 3x^2 + 3 + 2 = 3x^2 + 5[/tex]
The composite function is
[tex](f \circ g)(x) = 3x^2 + 5[/tex]
