Composite Functions

TL;DR

Composite functions involve substituting one function into another, either using multiplication or composition.

Transcript

now in this lesson we're going to talk about composite functions so let's say that f of x is equal to 3x minus 4 and that g of x let's say it's equal to x squared minus three what is f of g notice that this is different from f times g if you see a closed circle it's multiplication it's 3x minus 4 times x squared minus 3. but if you see like an open... Read More

Key Insights

• 👶 Composite functions involve substituting one function into another, resulting in a new function.
• ⭕ An open circle represents composition, while a closed circle represents multiplication.
• 💦 When evaluating composite functions, substitute the given value into the innermost function and work outward.
• 🪈 The order of composition matters. f(g(x)) is not necessarily the same as g(f(x)).
• 😑 Expanding and simplifying the expression is necessary when evaluating composite functions.
• 😑 Composite functions can be evaluated for specific values by substituting the values into the expression.
• 🛟 Composite functions can be used to model real-life situations, such as population growth or financial investments.

Questions & Answers

Q: What is a composite function?

A composite function involves substituting one function into another. It can be represented using an open circle and is different from multiplication.

Q: How do you find f(g(x))?

To find f(g(x)), replace x in f(x) with g(x) and simplify the resulting expression by expanding and combining like terms.

Q: What is the difference between an open circle and a closed circle in composite functions?

An open circle represents composition, indicating that one function is inside another. A closed circle represents multiplication, indicating the product of two functions.

Q: How do you evaluate composite functions?

To evaluate composite functions, substitute the given value into the innermost function, and then proceed with substituting the intermediate results into the outer functions until you reach the final result.

Summary & Key Takeaways

• Composite functions involve substituting one function into another.

• Using an open circle represents composition, while a closed circle represents multiplication.

• To find f(g(x)), replace x in f(x) with g(x), and then simplify the expression.