Math Problem Statement

Find f(x) + g(x), where f(x) = 4x^2 - 5x^4 and g(x) = 2x^2 + 3x^3 - x^4.

Solution

The question asks to find f(x)+g(x)f(x) + g(x), where:

f(x)=4x25x4f(x) = 4x^2 - 5x^4

g(x)=2x2+3x3x4g(x) = 2x^2 + 3x^3 - x^4

To find f(x)+g(x)f(x) + g(x), add the corresponding terms:

  1. Combine 4x24x^2 from f(x)f(x) and 2x22x^2 from g(x)g(x): 4x2+2x2=6x24x^2 + 2x^2 = 6x^2

  2. Combine the 5x4-5x^4 from f(x)f(x) and x4-x^4 from g(x)g(x): 5x4x4=6x4-5x^4 - x^4 = -6x^4

  3. Add the 3x33x^3 term from g(x)g(x) (no corresponding term in f(x)f(x)): 3x33x^3

Thus, the result is:

f(x)+g(x)=6x2+3x36x4f(x) + g(x) = 6x^2 + 3x^3 - 6x^4

Would you like more explanation or have questions? Here are five related questions to expand your understanding:

  1. How do you subtract two functions instead of adding them?
  2. How do you handle multiplication of two functions, such as f(x)g(x)f(x) \cdot g(x)?
  3. What are the implications of higher-degree terms like x4x^4 in polynomial functions?
  4. How does function addition apply to real-world problems?
  5. Can f(x)+g(x)f(x) + g(x) be graphed? How would it look visually compared to f(x)f(x) and g(x)g(x)?

Tip: Always align similar powers of xx when adding or subtracting pol

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Math Problem Analysis

Mathematical Concepts

Algebra
Polynomial Functions
Function Addition

Formulas

f(x) = 4x^2 - 5x^4
g(x) = 2x^2 + 3x^3 - x^4
f(x) + g(x) = (4x^2 - 5x^4) + (2x^2 + 3x^3 - x^4)

Theorems

Addition of Polynomial Functions

Suitable Grade Level

Grades 9-11