Understanding Math Composition | Exploring how combining functions creates new mathematical possibilities

4) Find the composition of the function.

To find the composition of two functions, let’s suppose we have two functions f and g

To find the composition of two functions, let’s suppose we have two functions f and g. The composition of f and g is denoted as (f ∘ g)(x) and it is defined as follows:

(f ∘ g)(x) = f(g(x))

In simpler terms, the composition function takes the value of x, applies g to it, and then uses the result of g as the input for f.

To illustrate this concept, let’s work through an example:

Suppose we have the following two functions:

f(x) = 2x + 3
g(x) = x^2

To find the composition (f ∘ g)(x), we need to substitute g(x) into f(x). First, we determine what g(x) is:

g(x) = x^2

Now, substitute g(x) into f(x):

(f ∘ g)(x) = f(g(x))
= f(x^2)
= 2(x^2) + 3
= 2x^2 + 3

Therefore, the composition (f ∘ g)(x) is equal to 2x^2 + 3.

The composition of functions allows us to combine multiple functions to create new functions. It is an important concept in mathematics and has various applications in calculus, linear algebra, and more.

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