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) = and g(x) = x - 8.

Choices:

A. x - 8

B.

C.

D.

Correct Answer: B

Solution:

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

Step 2:

Step 3:

Step 4:

Related Terms for Composition of Functions

• Function

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