Math Problem Statement

g(x) = x3 − x h(x) = (x3 − x)4 f(x) = 7(x3 − x)4

Solution

We have three functions defined as follows:

  1. g(x)=x3xg(x) = x^3 - x
  2. h(x)=(x3x)4h(x) = (x^3 - x)^4
  3. f(x)=7(x3x)4f(x) = 7(x^3 - x)^4

Would you like to find derivatives, solve these functions for particular values of xx, or explore any specific properties of these functions (such as critical points, maximums, minimums, etc.)?

Here are some potential next steps:

  1. Would you like to differentiate g(x)g(x), h(x)h(x), or f(x)f(x)?
  2. Would you like to expand h(x)h(x) or f(x)f(x) for simpler forms?
  3. Are you interested in solving g(x)=0g(x) = 0, h(x)=0h(x) = 0, or f(x)=0f(x) = 0?
  4. Do you need to evaluate these functions for specific values of xx?
  5. Should we analyze the graph or behavior of these functions?

Tip:

Always simplify a function before differentiating or integrating, as it makes the process more manageable!

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Functions
Function Composition
Exponentiation

Formulas

g(x) = x^3 − x
h(x) = (x^3 − x)^4
f(x) = 7(x^3 − x)^4

Theorems

Power Rule for Derivatives
Chain Rule for Derivatives

Suitable Grade Level

Grades 10-12