finding domain and range

[rioean17]

how do you find the domain and range of

f(x)=5^(sqrt(2x^2-1))


i can't seem to find them.

 

[pka]

Assuming that we are in the real number field then the standard rules apply.
You need \(\displaystyle 2x^2 - 1 \ge 0\).
Now for any \(\displaystyle b > 0\) and \(\displaystyle b \not=1\) we have the range of \(\displaystyle b^x\) to be \(\displaystyle (0,\infty ).\)

 

[rioean17]

so what you are saying is that the range is (0, infinty)

then what is the domain?

 

[pka]

so what you are saying is that the range is (0, infinty)

then what is the domain?

We are not here to do your homework for you.
You solve \(\displaystyle 2x^2 - 1 \ge 0\)!
We will check it for you.
But don't expect us to do it for you.

 

[rioean17]

i wasn't asking for the answer, i was asking on how to do it. i understand it know. also when i was graphing it on the calculator it shows that the range does not include (x,0) where the y value is zero, but when i worked out to find the range i got the same answer for the range (0,infinty) but how is that if on the graph it doesnt include 0

 

[pka]

I think that you should throw the calculator away and learn the mathematics behind this problem.

The point is that 0 is not in the range. To what power can one raise 5 in order to get 0: NONE!

 

[rioean17]

that is why i was confused, you don't need to be mean about it. i was only using the calculator to check my work. why do you think i posted the question in the first place. it was to get help on how to figure it out, not to get the answer. how am i going to be able to answer another problem like this if i dont know what im doing.

 

[stapel]

The tutors aren't "being mean". They are trying to explain the mathematics, and you are responding with calculators. The reason it is being suggested that you put the calculator aside and learn the mathematics is because, in order to answer these questions appropriately, you need the mathematics. The pretty picture on the screen can only tell you just so much.

I apologize if this causes offense, but I'm afraid you really do need to learn the mathematics.

Eliz.

 

[rioean17]

i realize i need to learn the mathematics, that is why i aked the question in the first place. but noone has yet to explain to me on how to find the domain and range in an easy to understand manner.

 

[galactus]

\(\displaystyle \L\\5^{\sqrt{2x^{2}-1}}\)

The domain is the numbers you put in. The range is what comes out.

Try the numbers between \(\displaystyle \frac{-1}{\sqrt{2}}\) and \(\displaystyle \frac{1}{\sqrt{2}}\).

See what you get?.

In other words, what values result in a negative inside your radical.

That would result in a complex value. Right?.

Those will NOT be in the domain.

 

[pka]

so what you are saying is that the range is (0, infinty)
then what is the domain?

When you wrote that, it seemed to me as if you were demanding an answer not an explanation.

but none has yet to explain to me on how to find the domain and range in an easy to understand manner.

First, surely if you are expected to find domains & ranges you must have received instruction on these topics. It is not our habit to do tutorials here. That is, we do not teach the material on this website. We try to help you. But we also expect that you know how to do the basics of any question that you ask. Do you understand how we work here?