Question

1. (cos^4(x) = f(g(x))) where (f(x) = square), and (g(x) = square).

Explanation:

Step1: Identify the inner function

The expression is \(\cos^4(x)\), which can be seen as raising \(\cos(x)\) to the 4th power. So the inner function \(g(x)\) should be the function inside the composition, which is \(\cos(x)\).

Step2: Identify the outer function

The outer function \(f(x)\) should be the function that takes the result of \(g(x)\) and raises it to the 4th power. So if \(g(x)=\cos(x)\), then \(f(x)\) should be \(x^4\) because when we substitute \(g(x)\) into \(f(x)\), we get \(f(g(x)) = (\cos(x))^4=\cos^4(x)\).

Answer:

\(f(x) = x^4\), \(g(x)=\cos(x)\)