Functions 8 - Composite functions
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Lesson Summary:
In this lesson on composite functions, we learn how to write a function as a composition of two other functions. Starting with two given functions, we learn how to write a composite function by plugging in one function to the other. Then, we practice breaking down complex functions into simpler composite functions using the given functions. These problems are challenging, but with practice, we can develop the skills to master composite functions.
Lesson Description:
Writing expressions as a composite of pre-defined functions.
More free YouTube videos by Julie Harland are organized at http://yourmathgal.com
Questions answered by this video:
- What are composite functions?
- How do you write variable expressions as a composition of pre-defined functions?
- If f(x) = 5x, g(x) = square root of x, and h(x) = x^2 - 3, how do you write square root of (x^2 - 3) as a composition of f, g, and h?
- If f(x) = 5x, g(x) = square root of x, and h(x) = x^2 - 3, how do you write 25x^2 - 3 as a composition of f, g, and h?
- If f(x) = 5x, g(x) = square root of x, and h(x) = x^2 - 3, how do you write 5x^2 - 15 as a composition of f, g, and h?
- If f(x) = 5x, g(x) = square root of x, and h(x) = x^2 - 3, how do you write square root of 5x as a composition of f, g, and h?
- If f(x) = 5x, g(x) = square root of x, and h(x) = x^2 - 3, how do you write x - 3 as a composition of f, g, and h?
- If f(x) = 5x, g(x) = square root of x, and h(x) = x^2 - 3, how do you write 5*square root of x as a composition of f, g, and h?
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Staff Review
This lesson will show you how to take a variable expression or function and use some pre-defined functions to write the expression as a composition of the functions. Six different problems are shown in this lesson and the concept of going backward and coming up with the composition of functions that will result in a given expression is explained. This can be a very tricky skill to learn.
