Question

What is the domain and range of y?

Answer 1

The domain is all of the possible x values you can put into the equation
Range is all the possible y values you can obtain

Answer 2

See, all of that confuses me.

Answer 3

Do you know that the denominator of a fraction cannot be 0?

Answer 4

Yes, the denominator cannot be a fraction.

Answer 5

The denominator can be a fraction. It CANNOT be 0

Answer 6

D: x ≠ 0; R: y > 2 ? @Mertsj

Answer 7

What denominator do you have in your problem?

Answer 8

x-2

Answer 9

What value of x would cause that denominator to be 0?

Answer 10

2

Answer 11

So x cannot be 2 and we will exclude 2 from the domain.

Answer 12

Do you also know that the number under the radical cannot be negative?

Answer 13

No, i do not:/

Answer 14

Well, that is why you came here...to learn something. The radicand must be positive since we are operating within the set of real numbers.

Answer 15

Now I see that the radicand is a fraction and that its numerator is positive. Do you see that?

Answer 16

Yes

Answer 17

If the numerator of a fraction is positive and its denominator is negative, then the fraction will be negative. Do you agree?

Answer 18

Yes

Answer 19

That means that x-2 cannot be negative which means it must be positive or 0.
But we have already said earlier that the denominator cannot be 0.
So now we know that it must be positive.
Do you understand?

Answer 20

Yes!

Answer 21

So write x-2>0 and solve

Answer 22

so √1/(x-2>0) ?

Answer 23

x>2

Answer 24

The solution of x-2>0 is
x>2 and that is the domain of the function.

Answer 25

and y cannot be 0 ?

Answer 26

Yes. y cannot be 0 because it says that y is the positive root.

Answer 27

Now we know the domain and range of the original function. The problem asks for the domain and range of the inverse function so remember:
In the inverse function, the domain and range are reversed: The domain of the function is the range of the inverse and the range of the function is the domain of the inverse.