Step 1 of 3 : Use the following information to find $(f \circ g)(x)$.
\[
f(x)=x^{\frac{1}{3}}-4 \text { and } g(x)=(x+1)^{2}
\]
Answer 2 Points
\[
(f \circ g)(x)=
\]
So, \((f \circ g)(x) = \boxed{((x + 1)^{2})^{\frac{1}{3}} - 4}\)
Step 1 :Given the functions \(f(x)=x^{\frac{1}{3}}-4\) and \(g(x)=(x+1)^{2}\)
Step 2 :The composition of two functions, denoted as \((f \circ g)(x)\), means we need to substitute the function \(g(x)\) into the function \(f(x)\). In other words, wherever we see an \(x\) in \(f(x)\), we replace it with the entire function \(g(x)\).
Step 3 :Substituting \(g(x)\) into \(f(x)\) gives us \(((x + 1)^{2})^{\frac{1}{3}} - 4\)
Step 4 :So, \((f \circ g)(x) = \boxed{((x + 1)^{2})^{\frac{1}{3}} - 4}\)