Introduction to Function Composition | Summary and Q&A

TL;DR

Function composition is an operation that combines two functions to create a new function.

Key Insights

• 👶 Function composition is an operation that combines functions to form a new function.
• ❓ It involves substituting the output of one function into another function.
• ❓ Function composition can be challenging to understand initially but becomes easier with practice.
• 😃 The notation for function composition is f o g(x) or g o f(x).
• 🪈 It is essential to follow the order of operations when composing functions.
• 🫨 Function composition is akin to plugging one function into another.
• ❓ By composing functions, we can represent complex relationships between variables.

Transcript

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Questions & Answers

Q: What is function composition?

Function composition is an operation that combines two functions to create a new function. It involves substituting the output of one function into another function.

Q: How do you perform function composition?

To compose functions, replace the inner function with the outer function and simplify. For example, if f(x) = x + 2 and g(x) = 3x, then f o g(x) means replacing g(x) in f(x) to get f(g(x)) = 3x + 2.

Q: Can you provide an example of function composition?

Sure! Let's compute f o g(x) with f(x) = x + 2 and g(x) = 3x. First, substitute g(x) into f(x), giving f(g(x)) = (3x) + 2 = 3x + 2.

Q: How does function composition work in the reverse order?

When performing G o F(x), you substitute f(x) into g(x). For example, if f(x) = x + 2 and g(x) = 3x, then G o F(x) becomes g(f(x)) = 3(x + 2) = 3x + 6.

Summary & Key Takeaways

• Function composition allows combining two functions, just like adding, subtracting, multiplying, or dividing numbers.

• To compose functions, replace the inner function with the outer function and simplify.

• Function composition can be challenging to grasp initially but becomes clearer with practice.