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Determine the interval on which f(x) = the square root of the quantity of x plus 2 is integrable.

(−∞, 2)
[−2, ∞)
(−∞,−2) U (−2, ∞)
All reals

Determine the interval on which fx the square root of the quantity of x plus 2 is integrable 2 2 2 U 2 All reals class=

Respuesta :

iBrainly
i'm thinking that the answer is b 
 
Domain: [-2,infin), {x|x > (or equal to) -2}

Answer:

The interval on which f(x) is integrable is:

                             [-2, ∞)

Step-by-step explanation:

We are given a function f(x) as:

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

We know that a function is integrable over a given interval if it is continuous over a given interval.

Now, we know that the square root function is well defined if the function under the square root sign is positive.

This means here the function is well defined if:

[tex]x+2\geq 0[/tex]

i.e.

[tex]x\geq -2[/tex]

Also, the square root function is continuous over it's domain.

and hence it is integrable over it's domain.

This means that the function is integrable over:

                       [-2,∞)

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