Question

Select the correct answer. If f(x)=2-x^1/2 and g(x)=x^2-9 , what is the domain of g(x) ÷ f(x)

Answer 1

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

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 ; +∞[

Answer 2

[0,4) U (4,+∞)

EXPLANATION

The given functions are:

`f(x)=2- √(x)`

and

`g(x) = {x}^(2) - 9`

We want to find the domain of:

`g(x) / f(x) = \frac{ {x}^(2) - 9}{2 - √(x) }`

This function is defined for:

`2 - √(x) \\e0`

`2 \\e \: √(x)`

Square both sides,

`{2}^(2) \\e \: ({√(x)})^(2)`

`4 \\e \: x`

Also
`x\:\ge0`

Therefore the domain is

[0,4) U (4,+∞)