Given f(x) = 3 + 4x - x* and g(x) = 4x - 2, find the g - f

It seems there might be a typo in the function \( f(x) = 3 + 4x - x* \). It’s not clear what “\( x* \)” represents. Could you please clarify or confirm if you meant something else, such as \( x^2 \) or \( x \cdot \)? Once I have the correct function definition, I can proceed with finding \( g(x) - f(x) \).

If you meant:

1. \( f(x) = 3 + 4x - x^2 \) (if “\( x* \)” refers to \( x^2 \))
2. \( f(x) = 3 + 4x - x \cdot \text{constant} \) (if “\( x* \)” refers to some constant multiplier of \( x \))

Please confirm or provide the correct definition.

Here are 5 related questions to consider:

1. If \( f(x) = 3 + 4x - x^2 \), what is the result of \( g(x) + f(x) \)?
2. How would you find \( g(f(x)) \) using the given functions?
3. What is the derivative of \( g(x) \) with respect to \( x \)?
4. What is the value of \( g(x) \) when \( x = 0 \)?
5. If \( f(x) = x \) instead, what would \( g(x) - f(x) \) be?

**Tip:** Always double-check for typos or unclear symbols in mathematical expressions to ensure accurate problem-solving.

Learn how to subtract two functions, g(x) = 4x - 2 and f(x) = 3 + 4x - x^2. This problem demonstrates the process of function subtraction, combining like terms, and simplifying polynomial expressions. Suitable for students in Grades 9-11.

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