Question

decompose the function y = √(2x³ - 4) in the form y = f(u) and u = g(x). (use g(x)=2x³ - 4)
provide your answer below:

1. y =
2. u =

Explanation:

Step1: Identify inner - outer functions

Given $y = \sqrt{2x^{3}-4}$ and $g(x)=2x^{3}-4$. We can consider $u = g(x)$ as the inner function and $y = f(u)$ as the outer function.

Step2: Define $f(u)$

Since $y=\sqrt{2x^{3}-4}$ and $u = 2x^{3}-4$, then $y = f(u)=\sqrt{u}$.

Step3: Recall $g(x)$

We are given that $u = g(x)=2x^{3}-4$.

Answer:

1. $y=\sqrt{u}$
2. $u = 2x^{3}-4$