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

Let g(x) = x / (8-x) and h(x) = x^3 - 4x^2 + 4. Calculate the function g(h(t)). g(h(t)) =
Transcript text: Let $g(x)=\frac{x}{8-x}$ and $h(x)=x^{3}-4 x^{2}+4$. Calculate the function $g(h(t))$. \[ g(h(t))= \]
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Solution

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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 \( g(x) = \frac{x}{8-x} \).
Step 1: Calculate \( h(t) \)

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

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

Step 2: Substitute \( h(t) \) into \( g(x) \)

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

\[ \boxed{-0.3333} \]

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