Explain the difference between function composition and application?

 Function composition involves chaining  two or more functions to create a new function. For example, if you have two functions, f(x) and g(x), their composition would be denoted as f(g(x)). 

Function application, on the other hand, is simply applying a function to an argument to produce a result. For example, if you have a function f(x) and you apply it to the argument 5, you get f(5), which would give you a result based on the function's definition.

So, in summary, function composition combines functions, while function application applies a function to an argument to produce a result.

Sure, let's use some concrete examples to illustrate both function composition and application.

Example.

1. **Function Composition:**

   Let's say we have two functions:

   - \( f(x) = 2x \)

   - \( g(x) = x^2 \)

   The composition of these functions, denoted as \( f(g(x)) \), means we first apply the function \( g(x) \) to an input \( x \), and then we apply the function \( f(x) \) to the result. So, \( f(g(x)) = f(x^2) = 2x^2 \).

2. **Function Application:**

   Let's use the same functions:

   ( f(x) = 2x \)

   - \( g(x) = x^2 \)

   If we apply the function \( f(x) \) to the argument \( x = 3 \), we get \( f(3) = 2 \times 3 = 6 \).

   If we apply the function \( g(x) \) to the argument \( x = 3 \), we get \( g(3) = 3^2 = 9 \).

These examples illustrate the difference between composing functions and applying functions. In function composition, we combine functions together, while in function application, we simply use a function to compute a result for a given input.

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