Answer: [tex](f\circ g)(x)=3x^2+5[/tex]
Step-by-step explanation:
We know that if f and g are functions, then the composite function of f and g is defined by :-
[tex](f\circ g)(x)=f(g(x))[/tex]
Given: If [tex]f(x) = 3x + 2\ and\ g(x) = x^2 + 1[/tex]
Then, [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]
Hence, [tex](f\circ g)(x)=3x^2+5[/tex]
