Section 2.4 Operations with Functions.pdf - 2.4 Operations...

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Unformatted text preview: 2.4 Operations with Functions Operations with Functions ( + )() = () + () ( ∙ )() = () ∙ () ( − )() = () − () () () () = () , () ≠ 0 The domain of + , − , and ⋅ is the intersection of the domains of and . The domain of is the intersection of the domains of and , for () ≠ 0. Ex 1) Let () = 2 − 3 and () = 4 + 5. Find each of the following: a) ( + )() and its domain b) ( − )() and its domain c) ( ⋅ )() and its domain d) ( ) () and its domain Ex 2) Let = {(−3,1), (0,4), (2,0)} and = {(−3,2), (1,2), (2,6), (4,0)}. Find each function and state the domain. a) − b) Ex 3) Let () = 3 + 4 and () = −||. Evaluate the following: a) ( + )(2) b) ( ⋅ )(−3) Composition of Functions ( ∘ )() = (()) ( ∘ )() = (()) The domain of ∘ is the intersection of the domains of and ∘ . The domain of ∘ is the intersection of the domains of and ∘ . Ex 4) Let () = √ − 1 and () = 2 + 5. a) Find ( ∘ )() and its domain b) Find ( ∘ )(3) c) Find ( ∘ )() and its domain Ex 5) Given () = √ + 5, find two functions () and ℎ() such that = ℎ ∘ . Ex 6) Let () = +6 7 , () = 3 + 2 , ℎ() = ( − 23)3 . Find ( h g f )(29) Ex 7) Let = 52 + 9 and = − 3. Write as a function of . Ex 8) Let () = 2 − 5 and () = √ + 8. Find each of the following and its domain: a) ( ∙ )() b) (/)() c) (/)() d) ( ∘ )() ...
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