Express the given function \( h \) as a composition of two functions \( f \) and \( g \) so that \( h(x)=(f \circ g)(x) \), where one of the functions is \( x^{4}-3 \). \( h(x)=\sqrt[7]{x^{4}-3} \) \( f(x)=x^{6} \) (Simplify your answer.)

To express the function \( h(x) = \sqrt[7]{x^{4}-3} \) as a composition of two functions, where one of the functions is \( x^{4} - 3 \), we can identify \( g(x) = x^{4} - 3 \) and then define \( f(x) \) based on the output of \( g(x) \). Now, using the definition of \( f \) given as \( f(x) = x^{6} \), we can rewrite \( h \): 1. \( g(x) = x^{4} - 3 \) 2. Since we need to take the seventh root of \( g(x) \) for \( h(x) \), which is equivalent to raising \( g(x) \) to the power of \( \frac{1}{7} \), we define: \( f(y) = y^{\frac{1}{7}} \) for \( y = g(x) \). Now we combine them to represent \( h(x) \): \[ h(x) = f(g(x)) = f(x^{4} - 3) = (x^{4} - 3)^{\frac{1}{7}} \] Thus, we can present the composition as: \[ h(x) = f(g(x)) \quad \text{where} \quad g(x) = x^{4} - 3 \quad \text{and} \quad f(y) = y^{\frac{1}{7}}. \] So, \( (f \circ g)(x) = (x^{4} - 3)^{\frac{1}{7}} \).