CHAPTER 1
1.4 COMBINATIONS OF FUNCTIONS
OBJECTIVES
• Students will learn about:
• Add, subtract, multiply and divide functions.
• Find compositions of one function with another
function.
ARITHMETIC COMBINATIONS OF
FUNCTIONS
• Just like we can combine two numbers by any of the
operations . Two functions can be combine to create
new functions.
• The sum,difference,product and quotient of functions.
• Sum of f + g
(f + g)(x) = f(x) + g(x)
• Difference of f - g
(f - g)(x) = f(x) - g(x)
• Product of f g
(f . g)(x) = f(x)g(x)
• Quotient of f/ g
(f /g)(x) = f(x)/g(x)
EXAMPLE 1
• Given f(x) = x2 − x − 6 and g(x) = x + 2, find each
function.
EXAMPLE 2
𝟏
𝒙
• Given f(x) = x2 − 3 and 𝒈 𝒙 = , find each function
EXAMPLE 3
Given f(x) = 3x − 3 and 𝒈 𝒙 = 𝟐𝒙, find
each function
STUDENT GUIDED PRACTICE
• Let 𝑓 𝑥 = 𝑥 2 𝑎𝑛𝑑 𝑔 𝑥 = 𝑥 + 1 find each function
operation
EXAMPLE 4
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Problem 1 from function operation worksheet
𝑔 𝑛 = 𝑛2 + 4 + 2𝑛
ℎ 𝑛 = −3𝑛 + 2
𝑓𝑖𝑛𝑑 (𝑔. ℎ)(1)
EXAMPLE 5
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Problem #2 from function operation worksheet
𝑓 𝑥 = 4𝑥 − 3
𝑔 𝑥 = 𝑥 3 + 2𝑥
𝑓𝑖𝑛𝑑 (𝑓 − 𝑔)(4)
COMPOSITION OF FUNCTIONS
• In a function composition, the result of one function
is used to evaluate a second function.
• Given functions f and g, the composite function f º
g can be described by the equation [f º g](x) =
f[g(x)]. The domain of f º g includes all x-values in
the domain of g for which g(x) is in the domain of f.
EXAMPLE 6
• Example Given f(x) = 3x2 + 2x − 1 and g(x) = 4x + 2,
find [f º g](x) and [g º f](x).
EXAMPLE 7
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Problem 8 form function operations worksheet
Given:
𝑔 𝑛 = 3𝑛 + 2
𝑓 𝑛 = 2𝑛2 + 5
• 𝑓𝑖𝑛𝑑 𝑔 𝑓 2
STUDENT GUIDE
• Do all problems form function operations worksheet
HOMEWORK
• Do problems 11-22 from your book page 117
CLOSURE
• Today we learn about how function operation
works and also we learned about combination of
functions.