Question

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

Explanation:

Step1: Identify the outer function

The given composite function is $\cos(x^4)$. The outer function $f(x)$ should be the cosine function, so we can take $f(x) = \cos(x)$.

Step2: Identify the inner function

The inner function $g(x)$ is the function that is inside the cosine function. Here, the expression inside the cosine is $x^4$, so we take $g(x) = x^4$. We can verify this by substituting $g(x)$ into $f(x)$: $f(g(x)) = f(x^4) = \cos(x^4)$, which matches the given function.

Answer:

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