If f(x) = x^4 + x^3 + x^2 and g(x) = x^2 where x ≠ 0, what is f(g(x))?

To find f(g(x)), we first need to substitute g(x) into f(x).

Given:

• f(x) = x⁴ + x³ + x²
• g(x) = x²

Now, we substitute g(x) into f(x):

f(g(x)) = f(x²)

Now, replace every x in f(x) with x²:

f(x²) = (x²)⁴ + (x²)³ + (x²)²

Calculating each term:

• (x²)⁴ = x⁸
• (x²)³ = x⁶
• (x²)² = x⁴

Now combine all the terms:

f(g(x)) = x⁸ + x⁶ + x⁴

So, the final answer is:

f(g(x)) = x⁸ + x⁶ + x⁴