Question

what would the domain of x/2-x be?

Answer 1

did you mean, x/(2-x)

or

(x/2) - x

Answer 2

is this
\[\frac{x}{x-2}\]? if so all real numbers except 2

Answer 3

because you still cannot divide by zero

Answer 4

oh so do you only look at the denominator to figure out the domain?

Answer 5

for this one....
\[k(x)=\sqrt{x/2-x}\]

Answer 6

Domain really only considers two major elements: denominators of fractions cannot be zero (divide by 0 problem), and even radicals (such as square roots, 4th roots, etc) cannot be taken of negative values.

For the problem of x/(2-x), the answer of all reals except 2 is correct.

For the radical problem, you must also consider that the radicand must be greater than or equal to zero, or solve this inequality:
\[x/2 - x \ge 0\]

Answer 7

\[x \le -2\]

Answer 8

Eliza27: Not correct for the radical problem proposed by desireeee11. Try x = 0 in the radical expression...it will not cause a domain violation. (k(0) = 0)

Perhaps an algebra error?

Answer 9

yes you only look at the denominator if you have a rational function

Answer 10

Oh yeah I though the 0 was a 1 thanks

Answer 11

if you have a radical inside must
\[\geq 0\]

Answer 12

"radicand" is the corect word

Answer 13

but if it is really \[k(x)=\frac{x}{x-2}\]\] then solution is more complicated

Answer 14

i mean
\[k(x)=\sqrt{\frac{x}{x-2}}\]

Answer 15

then you have to make sure that
\[\frac{x}{x-2}\geq 0\]

Answer 16

solution would be
\[(\infty,0]\cup (2,\infty)\]

Answer 17

thank you