To find f(g(x)), we first need to determine what g(x) is when we substitute a value for x.
Given that g(x) = x^2, we can compute it by plugging in any valid value for x. Let’s keep it simple and use x = a (where a is any number other than 0), thus g(a) = a^2.
Now, we will substitute g(a) into the function f(x). The function f(x) is defined as:
f(x) = x^4 + x^3 + x^2 Replacing x in this function with g(a) = a^2, we have:
f(g(a)) = f(a^2) = (a^2)^4 + (a^2)^3 + (a^2)^2 This simplifies to:
f(a^2) = a^8 + a^6 + a^4 Thus, the final result for f(g(x)) is:
f(g(x)) = x^8 + x^6 + x^4 In conclusion, replacing x in f(g(x)) with x^2 leads us to the simplified expression:
x^8 + x^6 + x^4.