Respuesta :

dhiab

Answer:

the domain of g(x) ÷ f(x) is :D = ]-∞ ; 4[U] 4 ; +∞[

Step-by-step explanation:

g(x) ÷ f(x) exist for : 2-x^1/2 ≠ 0

 2-x^1/2 = 0

  x^1/2 = 2

  (x^1/2)² = 2²

x = 4

the domain of g(x) ÷ f(x) is :D = ]-∞ ; 4[U] 4 ; +∞[

kudzordzifrancis

ANSWER

[0,4) U (4,+∞)

EXPLANATION

The given functions are:

[tex]f(x)=2- \sqrt{x} [/tex]

and

[tex]g(x) = {x}^{2} - 9[/tex]

We want to find the domain of:

[tex] g(x) \div f(x) = \frac{ {x}^{2} - 9}{2 - \sqrt{x} } [/tex]

This function is defined for:

[tex]2 - \sqrt{x} \ne0[/tex]

[tex]2 \ne \: \sqrt{x} [/tex]

Square both sides,

[tex] {2}^{2} \ne \: ({\sqrt{x}})^{2} [/tex]

[tex]4 \ne \: x[/tex]

Also [tex] x\:\ge0[/tex]

Therefore the domain is

[0,4) U (4,+∞)

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