Explain the concept of composite functions with the help of an example.

In mathematics, a function means a relation between an input and output variable where, the output depends upon the input.

Answer: Composite function is a function that depends on any other function.

A composite function is created by composing one function within another function.

Explanation:

For any function, say g(x), we infer that "g of x"  is a function in terms of variable x.

Similarly, any function of the form f(g(x)) will be read as "f of g of x". 

The function f(g(x)) is a composite function here.

g is the inner function and f is the outer function.

It can also be represented as:

• (f∘g)(x)
• fg(x)

Let's look into an example to understand composite function

Example

If a function f(x) = 2x + 5 and another function g(x) = x - 6, can you find (f∘g)(x)? 

f(x) = 2x + 5

Substitute x = g(x) = x - 6

f(g(x))= 2(x - 6) + 5 = 2x - 7

Thus, (f∘g)(x) = 2x - 7

Therefore, composite function is a function that depends on any other function and is created by composing one function within another function.