Math Problem Statement

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

Solution

It seems there might be a typo in the function f(x)=3+4xxf(x) = 3 + 4x - x*. It’s not clear what “xx*” represents. Could you please clarify or confirm if you meant something else, such as x2x^2 or xx \cdot? Once I have the correct function definition, I can proceed with finding g(x)f(x)g(x) - f(x).

If you meant:

  1. f(x)=3+4xx2f(x) = 3 + 4x - x^2 (if “xx*” refers to x2x^2)
  2. f(x)=3+4xxconstantf(x) = 3 + 4x - x \cdot \text{constant} (if “xx*” refers to some constant multiplier of xx)

Please confirm or provide the correct definition.

Here are 5 related questions to consider:

  1. If f(x)=3+4xx2f(x) = 3 + 4x - x^2, what is the result of g(x)+f(x)g(x) + f(x)?
  2. How would you find g(f(x))g(f(x)) using the given functions?
  3. What is the derivative of g(x)g(x) with respect to xx?
  4. What is the value of g(x)g(x) when x=0x = 0?
  5. If f(x)=xf(x) = x instead, what would g(x)f(x)g(x) - f(x) be?

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

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Subtraction of Functions

Formulas

g(x) - f(x) = (4x - 2) - (3 + 4x - x^2)

Theorems

Subtraction of Functions
Polynomial Functions

Suitable Grade Level

Grades 9-11