Answer:
[tex](f\circ g)(4)=31[/tex]
Step-by-step explanation:
Composite Function
Given f(x) and g(x) real functions, the composite function named fog(x) is defined as:
[tex](f\circ g)(x)=f(g(x))[/tex]
For practical purposes, it can be found by substituting g into f.
We have:
[tex]f(x)=3x+1[/tex]
[tex]g(x)=x^2-6[/tex]
Computing the composite function:
[tex](f\circ g)(x)=f(g(x))=3(x^2-6)+1[/tex]
Operating:
[tex](f\circ g)(x)=3x^2-18+1[/tex]
Operating:
[tex](f\circ g)(x)=3x^2-17[/tex]
Now evaluate for x=4
[tex](f\circ g)(4)=3(4)^2-17=48-17[/tex]
[tex]\boxed{(f\circ g)(4)=31}[/tex]
