Function Operations and 2.8 Composition
2.8
Function Operations and Composition
Arithmetic Operations on Functions The Difference Quotient Composition of Functions and Domain
2.8 - 1
Operations of Functions
Given two functions and g, then for all values of x for which both (x) and g(x) are defined, the functions + g, ? g, g, and /g are defined as
follows.( f + g )( x ) =f (x) + g(x) Sum ( f - g )( x ) =f (x) - g(x) Difference
( fg )( x ) = f (x)g(x) Product
= gf ( x )
f (x), g(x)
g(x) 0 Quotient
2.8 - 2
Example 1 USING OPERATIONS ON FUNCTIONS
Let (x) = x2 + 1 and g(x) = 3x + 5. Find the following.
a. ( f + g )(1)
Solution Since (1) = 2 and g(1) = 8, use the definition to get
( f + g )(1) =f (1) + g(1) ( f + g )(x) =f (x) + g(x)
= 2+8 = 10
2.8 - 3
Example 1 USING OPERATIONS ON FUNCTIONS
Let (x) = x2 + 1 and g(x) = 3x + 5. Find the following.
b. ( f - g )(-3)
Solution Since (?3) = 10 and g(?3) = ?4, use the definition to get
( f - g ) (-3) = f (-3) - g(-3) ( f - g )(x) =f (x) - g(x)
= 10 - (-4)
= 14
2.8 - 4
Example 1 USING OPERATIONS ON FUNCTIONS
Let (x) = x2 + 1 and g(x) = 3x + 5. Find the following.
c. ( fg )(5)
Solution Since (5) = 26 and g(5) = 20, use the definition to get
( fg )(5) = f (5)g(5)
= 26 20
= 520
2.8 - 5
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