Questions: Let g(x) = x / (8-x) and h(x) = x^3 - 4x^2 + 4. Calculate the function g(h(t)). g(h(t)) =

Solution Steps

To find \( g(h(t)) \), we need to substitute \( h(t) \) into the function \( g(x) \). This involves two steps:

1. Calculate \( h(t) \) using the given function \( h(x) = x^3 - 4x^2 + 4 \).
2. Substitute the result of \( h(t) \) into \( g(x) = \frac{x}{8-x} \).

First, we need to calculate \( h(t) \) using the function \( h(x) = x^3 - 4x^2 + 4 \). For \( t = 2 \):

\[ h(2) = 2^3 - 4 \cdot 2^2 + 4 = 8 - 16 + 4 = -4 \]

Next, we substitute \( h(t) = -4 \) into the function \( g(x) = \frac{x}{8-x} \):

\[ g(-4) = \frac{-4}{8 - (-4)} = \frac{-4}{8 + 4} = \frac{-4}{12} = -\frac{1}{3} \approx -0.3333 \]

Final Answer