The expression \((h - g)(x) = h(x) - g(x)\) represents the difference between two functions \(h(x)\) and \(g(x)\). 

### Explanation:
- \((h - g)(x)\) means "the function obtained by subtracting \(g(x)\) from \(h(x)\)".
- This is equivalent to taking the value of \(h(x)\) and subtracting the value of \(g(x)\) from it.

### Example:
If \(h(x) = 4x^2\) and \(g(x) = x^2 + 2x\), then:
\[
(h - g)(x) = h(x) - g(x) = 4x^2 - (x^2 + 2x)
\]
Simplifying:
\[
(h - g)(x) = 4x^2 - x^2 - 2x = 3x^2 - 2x
\]

Would you like more details or have any questions? 

Here are some related questions:
1. How do you subtract two functions and simplify the result?
2. What is the difference between \((h - g)(x)\) and \((h \cdot g)(x)\)?
3. Can you subtract trigonometric functions like \(\sin(x)\) and \(\cos(x)\)?
4. How do you represent \((h - g)(x)\) on a graph?
5. What happens when you subtract a linear function from a quadratic function?
6. How do you find the zeros of the function \(h(x) - g(x)\)?
7. Can you explain how to subtract rational functions?
8. What is the derivative of \((h - g)(x)\) in terms of \(h(x)\) and \(g(x)\)?

**Tip:** When subtracting functions, be sure to distribute any negative signs properly, especially when dealing with polynomials or expressions with multiple terms.

Explore the mathematical expression (h - g)(x) = h(x) - g(x) and learn how to subtract functions effectively. This detailed explanation covers the difference between two functions, illustrating with examples such as polynomial functions. Suitable for advanced high school students and anyone interested in algebraic concepts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation