Question

Help me find the domain and range of this function.

Answer 1

\[f(x)=\sqrt{8-2x^2}\]

Answer 2

show me the work please

Answer 3

@zepdrix
@imqwerty
Please

Answer 4

Why not you do the work and we just guide you :)
For the domain, the expression inside the root should be positive.
The range will depend on the domain.

Answer 5

Because I don't have a lot of time and need to see the actual steps on how to do it.

-2x^2 + 8 >= 0
-2x^2 >= -8
x^2 >= 4

When i square root both sides, what am I supposed to do?

Answer 6

idk

Answer 7

I'm sure these exercises are meant to test you not us
When you have a inequality like that, first you solve for x (you'll get x=2 or x=-2)
So x>=2 or x<=-2
That should be your domain.

Answer 8

I'm sorry, but that's wrong

Answer 9

\(8-2x^2\ge 0\)

Solve that to get your answer.

Answer 10

we are not here to do your work for you, ask about any particular steps when you are confused.

Answer 11

Ok, so how did my textbook get an absolute value like this:
\[|x| \le 2\]

Answer 12

I don't understand :(

Answer 13

Well you see, I just followed you reasoning.
It seems you forgot to switch signs here
-2x^2 >= -8
x^2 >= 4 (should be x^2 <= 4)
When solved you get x<=2 and x>=-2
Which is equivalent to |x| <= 2

Answer 14

\(|x|\le 2\) is the exact same thing as \(-2\le x \le 2\)

Answer 15

This was probably a former lesson in which someone gave you the steps and thus you did not learn it. Maybe not, just a guess.

Answer 16

Hmm, so the part that I'm not getting is that when solving the equation, you get \[x \le \pm2\]
but how does one get \[x \ge 2\]

Answer 17

oops, i meant less than or equal to

Answer 18

so from \[x \le \pm 2\]
doesn't that mean x has to be both less than 2 and -2?
Sorry, inequality is my weakness

Answer 19

The notation \(x \le \pm 2\) is not correct.
Maybe solving x^2 <= 4 yourself will help you understand.

Answer 20

so how would I go about solving x^2 <= 4 ??

Answer 21

First solve the equation for x.

Answer 22

square root both sides?

Answer 23

yep

Answer 24

then whats the next step?

Answer 25

what do you get ?

Answer 26

x <= plus or minus 2

Answer 27

Yeah but not with the inequality sign, it false I already said it.
Should be with the equal sign.

Answer 28

ok, x = plus or minus 2, now what do I do?

Answer 29

DO you know how to do this?

Answer 30

Please :3
Instead of going through all that x^2 <= 4 putting square root \[\sqrt{x^2}\le \sqrt{4}\] So \[|x|\le|2|\] and thus \[|x|\le2\] because 2 is positive.