**Definition of Composition of Functions**

- Composition of Functions is the process of combining two functions where one function is performed first and the result of which is substituted in place of each
*x*in the other function.

**More about Composition of Functions**

- The composition of functions
*f*and*g*is written as*f*o*g*. - [
*f*o*g*](*x*) =*f*[*g*(*x*)] - Composition of functions is not commutative.
*f*[*g*(*x*)] is generally not equal to*g*[*f*(*x*)].

For example, consider*f*(*x*) = 2*x*and*g*(*x*) =*x*- 3.

*f*[*g*(*x*)] = 2(*x*- 3) = 2*x*- 6

*g*[*f*(*x*)] = (2*x*) - 3 = 2*x*- 3

*f*[*g*(*x*)] is not equal to*g*[*f*(*x*)].

Evaluate the composite function

f[g(x)] forf(x) = 3x^{2}+ 6 andg(x) =x- 8.

Choices:

A.x- 8

B. 3x^{2}- 48x+ 198

C. 3x^{2}- 2

D. 3x^{2}+ 6

Correct Answer: B

Solution:

Step 1:f[g(x)] =f[x- 8]

Step 2:= 3(x- 8)^{2}+ 6

Step 3:= 3(x^{2}- 16x+ 64) + 6

Step 4:= 3x^{2}- 48x+ 198.

- Function