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  1. A composite function is generally a function that is written inside another function. Composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x ”.

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  2. Learn the concept of function composition with eight illustrative examples. Understand how to create a "new" function from two given functions.

  3. A composite function is a function created when one function is used as the input value for another function. Essentially, the output of the inner function (the function used as the input value) becomes the input of the outer function (the resulting value).

  4. Example: f(x) = √x and g(x) = x 2. The Domain of f(x) = √x is all non-negative Real Numbers. The Domain of g(x) = x 2 is all the Real Numbers. The composed function is:

  5. A composite function is a function that is within another function. One function is substituted as the input to another function. For example f[ g(𝑥) ] means that g( 𝑥 ) is substituted into every 𝑥 in the function of f( 𝑥 ).

  6. Create a new function by composition of functions. Evaluate composite functions. Find the domain of a composite function. Decompose a composite function into its component functions.

  7. A composite function is a function that depends on another function. A composite function is created when one function is substituted into another function. For example, f (g (x)) is the composite function that is formed when g (x) is substituted for x in f (x). f (g (x)) is read as “f of g of x ”.

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