Suppose $f$ and $g$ are polynomials, and that $h(x)=f(g(x))+g(x)$. Find the degree of $g(x)$ given that the degree of $h(x)$ is $8$ and the degree of $f(x)$ is $4$.
+33614 "Suppose f and g are polynomials, and that h(x)=f(g(x))+g(x). Find the degree of g(x) given that the degree of h(x) is 8 and the degree of f(x) is 4."
f(x) = a*x4 + b*x3 + ...
g(x) = c*xn + d*xn-1 + ...
h(x) = a*(c*xn + d*xn-1 + ...)4 + b*(c*xn + d*xn-1 + ...)3 + ... + c*xn + d*xn-1 + ...
h(x) = a*c4*x4n + ....
Must have 4n = 8 hence n = 2
Degree of g(x) is 2.
