Function Composition: Combining Mathematics Functions To Create A New One

Composition of mappings

Applying one function to the results of another: The result of f() is sent through g() It is written: (g º f)(x).

Composition of mappings, also known as function composition, is a way of combining two functions to create a new function, which can then be used to transform input values into output values.

Let’s consider two functions, f(x) and g(x). The composition of these two functions is denoted by (fog)(x) and is read as f composed with g of x. To compute (fog)(x), we first apply the input x to g(x), then we take the output of g(x) and use it as input for f(x).

Mathematically, we can represent this as follows:

(fog)(x) = f(g(x))

In other words, the output of g(x) becomes the input of f(x), and the resulting output is (fog)(x).

It is important to note that the composition of mappings is not always commutative, meaning (fog)(x) may not be the same as (gof)(x). Therefore, it is crucial to ensure the order of the composition is correct.

Here is an example to illustrate function composition:

Let’s say we have two functions:

f(x) = 3x – 1 and g(x) = x^2

To find (fog)(x), we need to substitute g(x) into f(x):

(fog)(x) = f(g(x)) = f(x^2) = 3x^2 – 1

Therefore, (fog)(x) = 3x^2 – 1.

In conclusion, composition of mappings is an important concept in mathematics that allows us to combine two functions to create a new one. It is denoted by (fog)(x) and requires us to apply the input value to the second function before applying it to the first function.

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