Composite Functions

Students can learn about Composite Functions and How to Graph Composite Functions. Students can get help with Calculus problems involving Composite function from the online tutors.

In this article about Composite Functions, we will learn about Composite Functions and see about how to draw the graph for composite functions and how to get the composite functions. We shall discuss how to make the composite function and how to draw the resultant function on a graph sheet.

When two functions are f(X) and g(X), the composite function f(g) will be defined as f[g(x)].

Graphing composite functions

Below is given an example explained with graphical representation which will help you to understand the concept of graphing composite functions better:

Example:
Consider the following function f(x)=x+1 find `g(x)=x^2`
Solution:
To answer this f[g(x)]
Substitute the g(x) in f(x) function
`=f(x^2)`
Perform the f(x) function ie f(x)=x+1
here `x=x^2`
so `f(g(x))=x^2+1`

Since the function `y=f(x)=x^2+1`
The value of a y varies with respect to the x-value. Substitute different x-value to the function, the y value will be obtained. After getting y value make the values of x and y value in table format.
`f(x)=x^2+1`
`f(0)=0^2+1=1`
`f(1)=1^2+1=2`
`f(2)=2^2+1=5`
`f(3)=3^2+1=10`

x	0	1	2	3
y=f(x)	1	2	5	10

Assign the scale as per our co-ordinate points.
Scale:
In x-axis 1unit= 1 cm
In y-axis 1unit= 2 cm
Graph for the composite functions

Example Problems

Example: Consider the following function f(x)=2x+1 find `g(x)=x^2`
Solution: To answer this f[g(x)]
Substitute the g(x) in f(x) function
`=f(x^2)`
Perform the f(x) function ie f(x)=2x+1
here `x=x^2`
so `f(g(x))=2(x^2)+1`
Since the function `y=f(x)=2(x^2)+1`

The value of a y varies with respect to the x-value. Substitute different x-value to the function, the y value will be obtained. After getting y value make the values of x and y value in table format.
`f(x)=2(x^2)+1`
`f(0)=2(0^2)+1=1`
`f(1)=2(1^2)+1=3`
`f(2)=2(2^2)+1=9`
`f(3)=2(3^2)+1=17`

x	0	1	2	3
y=f(x)	1	3	9	17

Assign the scale as per our co-ordinate points.

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Scale:
In x-axis 1unit= 1 cm
In y-axis 1unit= 3 cm
Graph for the composite functions