Question

Find the domain
\[f(x)=\sqrt{2x-1}\]

Answer 1

solve\[2x+1 \ge 0\]

Answer 2

the number inside the radical must be greater than or equal to 0. So you do this \[2x - 1 \ge 0\] Solve for x and you get \[x \ge \frac{1}{2}\] Therefore the domain is \[[\frac{1}{2},\infty)\]

Answer 3

and how about just a simple \[f(x)=x ^{3}-2\] ?

Answer 4

^^ all real numbers

Answer 5

so confused... but thank you!

Answer 6

What are you confused about?

Answer 7

just what im supposed to do, i have a test tomorrow. theres one such as f(x)=\[1divx ^{2}+5x+6\]

Answer 8

just look for real numbers that are "legal' under the radical. In this case, you can't have negative square roots.

Answer 9

this server is killing me

Answer 10

\[\frac{1}{x^2 + 5x + 6}\]

Answer 11

yes

Answer 12

ok you will need to find what number(s) make the denominator 0 because division by 0 is undefined. So set \[x^2 + 5x + 6 = 0\] and solve for x

Answer 13

For fractions, you can't have zeros in the denominator. What are the roots of x^2 + 5x + 6? These are where the domain make the fraction undefined (i.e. 1/0)

Answer 14

thank youu!

Answer 15

(x+3)(x+2) so zero occurs at x=-3 and x=-2. So domain is all real except -3 and -2.

Answer 16

and for square roots, make it negative?

Answer 17

yes, no negatives allowed in square roots. That's it. That's all the rules for determining domains. :)

Answer 18

for square roots the number inside the radical MUST be greater or equal to 0.. Because if you take a square root of a negative number you get imaginary/complex numbers

Answer 19

thanks =)

Answer 20

So all you do is set what ever is inside the radical greater or equal to 0 and solve for the variable.

Answer 21

Thats all the rules.. No division by 0 and no negative square roots.

Answer 22

We want real solutions. In Complex domains, negative square roots are allowed and division by zero is also allowed (only if imaginary part is not) -- but that's an entirely other great story.

Answer 23

^ thats a ugly story lol :P

Answer 24

mhmk ill figure it out, thanks for all the help guys

Answer 25

np - keep it up!