In the field of Maths, when two functions are combined in a manner such that the output of one function becomes the input to another function, then this is known as a composite function.

Now, consider three sets – X, Y and Z and let *f : X → Y* and g: Y → Z.

The mapping will comprise of mappings with variables f and g is which are known to be the composition of mappings. These are denoted by *gof* and *fog.*

Therefore, we are mapping onto and into respectively. The composite function is denoted by:

(gof)(x) = g(*f (X) )*

Likewise, (*f*og) (x) = *f* (g(x))

This calculator will help you find the composition of the functions. In fact, it will also evaluate the composition at a specified point, if the need be.

Fog and Gof are the functional composites or simply the composite functions. Here, fog means F-compose-g of x written as (f o g)(x) or written as f(g(x)). Similarly, Gof stands for G-compose of g written as (g o f)(x) or written as g(f(x)).