Question

If f(x) = 3x2 and g(x) = 4x2+1, what is the degree of (fog)(x)?

Answer 1

Answer:

4

Step-by-step explanation:

To solve this problem let us first find $(fog)(x)$, 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):

$(fog)(x)=3g(x)^2\\\\(fog)(x)=3(4x^2+1)^2\\\\(fog)(x)=3(16x^4+8x^2+1)\\\\(fog)(x)=48x^4+24x^2+3$

We have to find the the degree of $(fog)(x)$, which is the largest exponent on one of the polynomial's terms. Notice that $48x^4$ 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 :)