Composition of Functions

In the previous post we have discussed about How to use Multiply Fractions Calculator and In today’s session we are going to discuss about Composition of Functions. In mathematics we use many types of functions such as one-one, onto, man- one and many more. Here we are going to discuss the composition of functions means collaboration of two or more functions. Composition of function states that, we have three non void sets A, B and C where f: A → B, g: B → C be two functions. It means f is a function from A to B. like that g is a function from B to C. (know more about Composition Functions, here

When we consider the f and g function mutually then a new function comes out that is from A to C. This function is known as composition of f and g and is represented by gof.

Let’s take an example that will show the composition of function.

Example 1: – Let f: R → R; f(x) = sin x and g : R → R; g(x) = x² find fog and gof.

Solution: –

Now (gof) (x) = g (f(x)) = g (sin x) = (sin x)² = sin² x

And (fog) (x) = f(g(x)) = f(x²) = sin x²

There are so many properties of composition of functions, some of them are defined below: –

-The theorems of function is not commutative that is fog!=gof.

-The composition of functions is associative, if f, g and h are three functions such that (fog)oh

And fo(goh) exist, then

(fog)oh = fo (goh)

-The composition of two bijection is a bijection that is if f and g are two bijection, then gof is also a bijection.

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