To find \( g(f(f(x))) \), we need to evaluate the composition of the functions \( g \), \( f \), and \( f \) as follows:

1. **First, find \( f(f(x)) \):**
   Given \( f(x) = x^3 \), we need to evaluate:
   \[
   f(f(x)) = f(x^3) = (x^3)^3 = x^9
   \]

2. **Next, find \( g(f(f(x))) \):**
   Given \( g(x) = 1 - 2x \), substitute \( x^9 \) for \( x \) in \( g(x) \):
   \[
   g(f(f(x))) = g(x^9) = 1 - 2(x^9) = 1 - 2x^9
   \]

Thus, the final expression for \( g(f(f(x))) \) is:
\[
g(f(f(x))) = 1 - 2x^9
\]

Would you like more details or have any questions?

### Related Questions:
1. How would you find \( f(g(x)) \) for the same functions?
2. What is the derivative of \( g(f(f(x))) \)?
3. How would \( g(f(x)) \) be computed in this case?
4. Can you find \( g^{-1}(x) \) and use it to solve \( g(f(f(x))) = 0 \)?
5. What happens to the function \( g(f(f(x))) \) as \( x \to \infty \)?

### Tip:
When composing functions, always work from the inside out. Evaluate the innermost function first, then proceed outward step by step.

Given: f(x) = x^3, g(x) = 1 - 2x. Find gff.

Learn how to find the composition of functions g(f(f(x))) where f(x) = x^3 and g(x) = 1 - 2x. This solution involves evaluating function composition step-by-step, covering key algebraic concepts and properties of exponents. Suitable for high school students in Grades 9-12.

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