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Composition of Functions (f o g)(x)

December 8, 2020 by sastry

Composition of Functions (f o g)(x)

The term “composition of functions” (or “composite function”) refers to the combining of functions in a manner where the output from one function becomes the input for the next function.
Composition of Functions (f o g)(x) 1 In math terms, the range (the y-value answers) of one function becomes the domain (the x-values) of the next function.

The notation used for composition is:
(f o g)(x) = f(g(x)) and is read “f composed with g of x” or “f of g of x”.
Composition of Functions (f o g)(x) 2
Composition of Functions (f o g)(x) 3 Notice how the letters stay in the same order in each expression for the composition.
f (g(x)) clearly tells you to start with function g (innermost parentheses are done first).
Composition of functions can be thought of as a series of taxicab rides for your values.
The example below shows functions f and g working together to create the composition .
Note: The starting domain for function g is being limited to the four values 1, 2, 3 and 4 for this example.

Composition of Functions (f o g)(x) 4

In the example above, you can see what is happening to the individual elements throughout the composition. Now, suppose that we wish to write our composition as an algebraic expression.

Examples :

Composition of Functions (f o g)(x) 5

Composition of Functions (f o g)(x) 6

Filed Under: Mathematics Tagged With: Composition of Functions (f o g)(x)

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