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2a. Determine (๐‘“ x ๐‘”)(๐‘ฅ) in simplified form and state its domain, given ๐‘“(๐‘ฅ) = ๐‘™๐‘œ๐‘”๐‘ฅ and ๐‘”(๐‘ฅ) =2 /๐‘ฅโˆ’6

2b. Determine (๐‘“ รท ๐‘”)(๐‘ฅ) in simplified form and state its domain, given ๐‘“(๐‘ฅ) = ๐‘ฅ + 8 and ๐‘”(๐‘ฅ) = โˆš๐‘ฅ โˆ’ 8 (square root is over the whole expression "x-8"

2c. Determine (๐‘“๐‘œ๐‘”)(๐‘ฅ) in simplified form and state its domain, given ๐‘“(๐‘ฅ) =
3/๐‘ฅโˆ’2 and ๐‘”(๐‘ฅ) =๐‘ฅ/2๐‘ฅโˆ’3

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Anonymous
2 answers

  1. (f*g)(x) = f(x)*g(x) = logx * (2/(x-6))
    (f+g)(x) = f(x)+g(x) = .....
    (fโ€ขg)(x) = f(g(x)) = 3/(g(x)-2) = 3/((x/(2x-3))-3) = (9-6x)/(5x-9)

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    oobleck

  2. Why do f (x) and g (x) add up in question 2b? shouldn't they be divided?

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    Howl

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