find the domain and range of the function.
f(x)=(square root of)2x^2-1

Question

find the domain and range of the function. 
f(x)=(square root of)2x^2-1

anonymous · Answer

To find the domain set what is inside the radical greater than or equal to 0 and solve for ]$$2x^2-1\ge0$$
$$2x^2\ge1$$
$$x^2\ge1/2$$
$$x \ge1/\sqrt{2}$$

anonymous · Answer

They might want you to get rid of the radical in the denominator so you would have to multiply by one
$$1/\sqrt{2}\times \sqrt{2}/\sqrt{2}$$
$$\sqrt{2}/2$$

anonymous · Answer

so my domain is only one number?

anonymous · Answer

and wouldn't it be plus or minus square root of 2/2, as that's what it looks like on my calculator?

anonymous · Answer

no it would be [$$\sqrt{2}/2$$,infinity)

anonymous · Answer

That did not turn out right.  It is supposed to be  [sqrt2/2, infinity)

anonymous · Answer

sorry to be dumb, but why?
it makes a weird v thing on my graph. wow. that sounded legit.

anonymous · Answer

Haha, you are not dumb.  First off when you have a radical the inside cannot equal 0 that is a no no in math and to find the domain you have to set what is inside the radical greater than or equal to 0 and solve.  Also, you were right about the negative my mistake but the domain would be (-infinity,-sqrt(2)]U[sqrt(2), infinity)
You bracket the -sqrt(2) and sqrt(2) because they are included in the domain and you parenthesis the infinity because they are not a def number.

anonymous · Answer

what happened to the 2 under the sqrt(2)?

anonymous · Answer

and the range??

anonymous · Answer

please?

anonymous · Answer

Which part about the 2?

anonymous · Answer

x=sqrt(2)/2?

anonymous · Answer

where it's divided by 2?

anonymous · Answer

oh my bad I accidentally left it off, it needs to be there

anonymous · Answer

okay.

anonymous · Answer

as for the range...
I got [1,infinity)
because the graph is undefined at 0
The way to find this is by plugging in 0 usually, but since that makes it equal 0 I used one and one worked.

anonymous · Answer

Do you understand what I wrote, it does seem a bit confusing

anonymous · Answer

i get it now!!!! total lightbulb moment. i plugged in some other problems in the book into my calculator and they make sense! thank you SO much. (but even though the graph is undefined at zero, we still use it for range. i guess you can do that with precal punks like us) = )

anonymous · Answer

Haha good, Im glad it flipped on!!! :)