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.
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:
Let's look into an example to understand composite function
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.