2. OBJECTIVES:
• Define composition of functions.
• Perform composition of functions.
• Evaluate functional problems using composition of functions.
3. Composition of Functions
• Operation of function that must have two functions,
namely 𝒇(𝒙) and 𝒈 𝒙 ; and then perform the indicated
operation to produce the result.
• Also defined as, “applying a function to another
function”.
4.
5. Example 1
𝑓 𝑥 = 3𝑥 − 1 and 𝑔 𝑥 = 𝑥 + 4
Find 𝑓 ∘ 𝑔 𝑥 .
• Insert the 𝒈(𝒙) function into the 𝒇 𝒙 function.
𝒇 ∘ 𝒈 𝒙 = 𝟑 𝒙 + 𝟒 − 𝟏
= 𝟑𝒙 + 𝟏𝟐 − 𝟏
= 𝟑𝒙 + 𝟏𝟏
6. Find an expression for 𝑓 ∘ 𝑔 𝑥 for the
following:
a) 𝒇 𝒙 = 𝒙𝟐 − 𝟔 𝒂𝒏𝒅 𝒈(𝒙) = 𝒙 + 𝟒
b) 𝒇 𝒙 = 𝒙 + 𝟑 𝒂𝒏𝒅 𝒈 𝒙 = 𝒙 − 𝟗
c) 𝒇 𝒙 = 𝟐𝒙 + 𝟒 𝒂𝒏𝒅 𝒈 𝒙 = 𝟖 − 𝟑𝒙
d) 𝒇 𝒙 =
𝟏
𝟐
𝒙 − 𝟒 𝒂𝒏𝒅 𝒈 𝒙 = 𝒙 + 𝟑