#17. How to Find the Sum(f + g), Difference(f - g), Product(fg), and Quotient(f/g) of Functions

TL;DR

Learn how to perform addition, subtraction, multiplication, and division on functions, and determine the domain of each operation.

Transcript

in this problem we're given two functions f of x and g of x and we're asked to find these other functions here f plus g f minus g f times g and f divided by g as well as the domain of each let's go ahead and go through each one individually first let's do f plus g so to find f plus g all you basically do is add them up the correct notation would be... Read More

Key Insights

• 🎭 Addition, subtraction, multiplication, and division can all be performed on functions.
• ➗ The domain for all operations, except division, is all real numbers.
• ➗ The domain for division excludes x = 0 to avoid division by zero.
• ☺️ The notation f plus g of x represents the sum of two functions.

Questions & Answers

Q: How do you find f plus g?

To find f plus g, add f(x) and g(x) together. The domain for f plus g is all real numbers.

Q: What is the formula for f minus g?

The formula for f minus g is f(x) minus g(x). Subtract g(x) from f(x) to find the result. The domain for f minus g is all real numbers.

Q: How do you calculate f times g?

Multiply f(x) and g(x) together to find f times g. The result will be 5x^3 + 35x^2. The domain for f times g is all real numbers.

Q: What is the domain for f over g?

The domain for f over g is all real numbers except for x = 0. The function is not defined at x = 0 due to division by zero.

Summary & Key Takeaways

• Addition: To find f plus g, simply add the two functions f(x) and g(x) together.

• Subtraction: To find f minus g, subtract g(x) from f(x).

• Multiplication: To find f times g, multiply f(x) and g(x) together.

• Division: To find f over g, divide f(x) by g(x).

• The domain for all operations is all real numbers, except for division where x cannot equal zero.