1. What is Function Multiplication (f g)(x)?

Definition: The product of two functions f(x) and g(x), denoted as (f g)(x), is defined as the multiplication of their outputs for the same input x.

Purpose: This operation is fundamental in algebra and calculus, used in various applications including physics, engineering, and economics.

2. How Does Function Multiplication Work?

The operation follows the formula:

Where:

• \( f(x) \) — First function
• \( g(x) \) — Second function
• \( x \) — Input value (variable)

Explanation: For each x in the domain, multiply the output of f(x) by the output of g(x).

3. Domain Considerations

Details: The domain of (f g)(x) is the intersection of the domains of f(x) and g(x). Both functions must be defined at x for (f g)(x) to be defined.

4. Using the Calculator

Tips:

• Enter functions using standard mathematical notation (e.g., "x^2 + 3*x - 2")
• Optionally provide an x value to compute the specific result
• Use parentheses for clarity in complex functions

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between (f g)(x) and f(g(x))?
A: (f g)(x) is multiplication (f(x)*g(x)), while f(g(x)) is function composition (applying g first, then f).

Q2: Can I multiply more than two functions?
A: Yes, the product of n functions f₁(x)*f₂(x)*...*fₙ(x) can be calculated similarly.

Q3: What operations are supported in the function inputs?
A: Standard operations: +, -, *, /, ^ (exponent), parentheses, and common math functions if properly implemented.

Q4: How do I represent exponents?
A: Use the caret symbol (^), e.g., "x^2" for x squared.

Q5: What if I get an error?
A: Check your function syntax and ensure all parentheses are properly closed.