Answer:
4
Step-by-step explanation:
To solve this problem let us first find [tex](fog)(x)[/tex], or find the function of f(x) in terms of g(x). All we have to do is replace x with g(x) in the function f(x):
[tex](fog)(x)=3g(x)^2\\\\(fog)(x)=3(4x^2+1)^2\\\\(fog)(x)=3(16x^4+8x^2+1)\\\\(fog)(x)=48x^4+24x^2+3[/tex]
We have to find the the degree of [tex](fog)(x)[/tex], which is the largest exponent on one of the polynomial's terms. Notice that [tex]48x^4[/tex] has the greatest exponent of 4.
Therefore, the degree of (fog)(x) is 4.
I hope this helps! Let me know if you have any questions :)
