Question

For what interval is the function
f(x) = (20 + \sqrt{x}) / (\sqrt{20 + x})

continuous?

Answer 1

Well, first was is the domain of this function?

Answer 2

what is

Answer 3

The domain of this function is [-20, infinity)

Answer 4

No, it's not.

Answer 5

No sorry

Answer 6

The domain it is: (-20,0]

Answer 7

Noo....

Answer 8

What?#$

Answer 9

Then what would it be? This is why I think it is that:
The domain of the numerator is [0, infinty)
The domain of the denominator is (-20, infinity)

The intersection of these two domains is (-20,0]

Answer 10

The intersection of the two domains is
[0, infinity)

Answer 11

Why?

Answer 12

Is -1 in both domains? Is -10 in both domains?

Answer 13

But is 1 in both domains?

Answer 14

for x greater than zero

Answer 15

Oh I see. It makes sense because the square root of x only accepts positive real numbers.

Answer 16

yes

Answer 17

And zero, yes.

Answer 18

Now, where is it continuous?

Answer 19

for every x greater than zero it will be continuous not at any specific point

Answer 20

Yes I understand, please help me out with my other question.

Answer 21

@sumbul What to you mean "not at any specific point"?

Answer 22

in full interval

Answer 23

the answer is [0,infty)
so every x greater-than or equal-to zero

Answer 24

it is continuous at 0

Answer 25

oh, you're right.