Understanding Composition of Functions | How to Combine Two Functions Using Math

Compose

Composing in mathematics refers to the operation of combining two functions to form a new function

Composing in mathematics refers to the operation of combining two functions to form a new function. Let’s say we have two functions, f and g. The composition of these functions, denoted as (f ∘ g)(x), means that we first apply g to the variable x, and then apply f to the result.

Mathematically, (f ∘ g)(x) = f(g(x))

To better understand the concept of composition, let’s consider an example. Suppose we have the functions f(x) = 2x + 3 and g(x) = x^2.

To find the composition (f ∘ g)(x), we substitute g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = f(x^2)

Now, we substitute f(x) into the expression:

(f ∘ g)(x) = 2(x^2) + 3

So, the composition of f and g is the function (f ∘ g)(x) = 2x^2 + 3.

Composition of functions can be useful in solving various mathematical problems. It allows us to combine the operations of different functions in a systematic way, making it easier to analyze and work with complex mathematical expressions.

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