Composition of Functions

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) = 2x and g(x) = x - 3.
  f[g(x)] = 2(x - 3) = 2x - 6
  g[f(x)] = (2x) - 3 = 2x - 3
  f[g(x)] is not equal to g[f(x)].
  

Solved Example on Composition of Functions

Evaluate the composite function f[g(x)] for f(x) = 3x² + 6 and g(x) = x - 8.
Choices:
A. x - 8
B. 3x² - 48x + 198
C. 3x² - 2
D. 3x² + 6
Correct Answer: B
Solution:
Step 1: f[g(x)] = f[x - 8]
Step 2: = 3(x - 8)² + 6
Step 3: = 3(x² - 16x + 64) + 6
Step 4: = 3x² - 48x + 198.

Related Terms for Composition of Functions

• Function