1. What is Function Subtraction?

Function subtraction creates a new function by subtracting the output values of two functions. For functions f and g, the subtraction (f - g)(x) is defined as f(x) - g(x) for all x in the domain of both functions.

2. How Does the Calculator Work?

The calculator uses the function subtraction formula:

Where:

• \( f(x) \) — First function
• \( g(x) \) — Second function
• \( x \) — Input value (optional for evaluation)

Explanation: The calculator combines the two functions algebraically and can optionally evaluate the result at a specific x value.

3. Importance of Function Operations

Details: Function operations like subtraction are fundamental in mathematics, used in calculus, physics, engineering, and other fields to model combined effects of different phenomena.

4. Using the Calculator

Tips: Enter valid mathematical expressions for f(x) and g(x). Use standard notation (e.g., "x^2" for x squared, "sin(x)" for sine). For evaluation, enter a numeric x value.

5. Frequently Asked Questions (FAQ)

Q1: What types of functions can I subtract?
A: You can subtract any functions that can be expressed mathematically - polynomial, trigonometric, exponential, etc.

Q2: How is the domain of (f - g) determined?
A: The domain is the intersection of the domains of f and g - where both functions are defined.

Q3: Can I subtract more than two functions?
A: Yes, subtraction is associative, so (f - g - h)(x) = f(x) - g(x) - h(x).

Q4: What if my functions have different variables?
A: The calculator assumes both functions use 'x' as the variable. Mixed variables may cause errors.

Q5: Why can't I see a graph of the result?
A: This calculator provides algebraic results. For graphing, use a dedicated graphing tool.