Question
Asked Dec 5, 2019
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Given the function f ( x ) = x/ sqroot(3 x − 12), determine the domain and range

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Expert Answer

Step 1
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The given function is, f(x) =: V3x – 12 For values ofx less than 4, the denominator of f(x) will have a negativeradical. Also f(x) is not defined for x= 4. Therefore, the domain off(x) is, (4, )

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Step 2
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Obtain the critical point of f(x) as shownbelow. 3 (х) 2/3х - 12 Зх—12 УЗх -12 — Г(*)- 3 f(x) -0— /3х- 12- = 0 (х) -0 2/3х - 12 2(3х-12) - Зх %30 бх-24 -Зх — 0 3х324 х%3D8

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Step 3
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Also, 16 - x f"(x) 4(x-4)° 3x– 12 At x = 8, f" (x) >0. Therefore, x = 8 is a minimum point. f(8)=: V3(8) –12 V24 – 12 213 4

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