CH 2.2.2 Operation on Functions (Composite) (1).pdf - CHAPTER 2 GRAPHS AND FUNCTIONS 2018-2019 WS CH 2.2.3 Operation on Functions 1 DEFINITION OPERATION

# CH 2.2.2 Operation on Functions (Composite) (1).pdf -...

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2018-2019 1 WS CH 2.2.3 Operation on Functions CHAPTER 2 GRAPHS AND FUNCTIONS
2018-2019 WS CH 2.2.3 Operation on Functions 2 Let ? and ? be functions with domains ? and ? . DEFINITION : OPERATION ON FUNCTIONS ? + ? 𝑥 = ? 𝑥 + ? 𝑥 ? − ? 𝑥 = ? 𝑥 − ? 𝑥 ?? 𝑥 = ? 𝑥 ? 𝑥 ? ? 𝑥 = ? 𝑥 ? 𝑥 Domain ? ∩ ? Domain ? ∩ ? Domain ? ∩ ? Domain 𝑥 ∈ ? ∩ ? ? 𝑥 ≠ 0
2018-2019 WS CH 2.2.3 Operation on Functions 3 EXAMPLE 1 : Let ? 𝑥 = 𝑥 3 and ? 𝑥 = 𝑥 Solution : a) Find the functions ? + ?, ? − ?, ?? 𝑎𝑛𝑑 ?/? and their domains b) Find ? + ? 4 , ? − ? 4 , ?? 3 and Τ ? ? 1 a) The domain of ? is −∞, ∞ The domain of ? is ሾ0, ? + ? 𝑥 = ? 𝑥 + ? 𝑥 = 𝑥 3 + 𝑥 Domain ∶ ሾ0, ? − ? 𝑥 = ? 𝑥 − ? 𝑥 = 𝑥 3 𝑥 Domain ∶ ሾ0,
2018-2019 WS CH 2.2.3 Operation on Functions 4 Solution : ?? 𝑥 = ? 𝑥 ? 𝑥 = 𝑥 3 𝑥 Domain ∶ ሾ0, ? ? 𝑥 = ?(𝑥ሻ ?(𝑥ሻ = 𝑥 3 𝑥 Domain ∶ 0, ∞ ? + ? 4 = ? 4 + ? 4 = 4 3 + 4 = 66 ? − ? 4 = ? 4 − ? 4 = 4 3 4 = 62 ?? 3 = ? 3 ? 3 = 3 3 3 = 27 3 ? ? 1 = ?(1ሻ ?(1ሻ = 1 3 1 = 1
2018-2019 WS CH 2.2.3 Operation on Functions 5 EXAMPLE 2 : Let ? 𝑥 = 𝑥 − 1 and ? 𝑥 = 4 − 𝑥 Solution : Find the ? + ?, ? − ?, ?? 𝑎𝑛𝑑 ?/?

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