Question

Determine o domínio das funções:

a) y= √x+3

b) y=2365/2x-8

c) y= 6/√4-2x

d) y= 60000000/√6x+18

e) y= 88978894/x^2-8x-9
Com todos os cálculos pfvr ​

Answer 1

Oie, Td Bom?!

a)

y = √[x + 3]

• √[x + 3]

x + 3 ≥ 0

x ≥ - 3

• x + 3

x∈IR

D = {x∈IR / x ≥ - 3}

b)

y = 2365/[2x - 8]

• 2365/[2x - 8]

2x - 8 = 0

2x = 8

x = 8/2

x = 4

x∈IR / {4}

• 2x - 8

x∈IR

D = {x∈IR / 4}

c)

y = 6/{√[4 - 2x]}

y = 6/{√[- 2x + 4]}

• 6/{√[- 2x + 4]}

√[- 2x + 4] = 0

- 2x + 4 = 0

- 2x = - 4 . (- 1)

2x = 4

x = 4/2

x = 2

x∈IR / {2}

• √[- 2x + 4]

- 2x + 4 ≥ 0

- 2x ≤ - 4 . (- 1)

2x ≤ 4

x ≤ 4/2

x ≤ 2

• - 2x + 4

x∈IR

D = {x∈IR / x < 2}

d)

y = 60000000/{√[6x + 18]}

• 60000000/{√[6x + 18]}

√[6x + 18] = 0

6x + 18 = 0

6x = - 18

x = - 18/6

x = - 3

x∈IR / {3}

• √[6x + 18]

6x + 18 ≥ 0

6x ≥ - 18

x ≥ - 18/6

x ≥ - 3

• 6x + 18

x∈IR

D = {x∈IR / x > - 3}

e)

y = 88978894/[x² - 8x - 9]

• 88978894/[x² - 8x - 9]

x² - 8x - 9 = 0

x² + x - 9x - 9 = 0

x . (x + 1) - 9(x + 1) = 0

(x + 1) . (x - 9) = 0

• x + 1 = 0 ⇒ x = - 1
• x - 9 = 0 ⇒ x = 9

x∈IR / {- 1 , 9}

• x² - 8x - 9

x∈IR

D = {x∈IR / - 1 , 9}

Att. Makaveli1996