How do you find the domain of equations? For example, how do you find the domain of y= x+2/x-4.. please show the scratch and not just the answer. thanks!

Question

chriss · Answer

In this problem the only restriction you have is that the denominator cannot be 0.  For the denominator to be 0, x would have to be 4.  So the domain is 
$$(-\infty,4) \cup (4,\infty)$$

anonymous · Answer

so, in general, how do you find the domain?

chriss · Answer

Well the domain is all of the possible inputs for an equation.  Generally that means x values.  So the idea is to determine what x values can be used in a function and get an answer.  In the problem you gave, that would be all real numbers except for 4 because x=4 would cause you to divide by zero and the answer would be undefined.  Any other real number however would work.

Another example where you would have a restriction on the domain would be
$$\sqrt{x}$$

In this case x would be restricted to the nonnegative integers or
$$(0,\infty)$$
because you can't take the square root of a negative number.

chriss · Answer

A more succinct answer to your question is that you start with all the real numbers as your domain and then try to determine if any subset of the real numbers needs to be excluded.  In your example, 4 is excluded, in my example all negative numbers are excluded.

anonymous · Answer

okay. thank you. so what would the domain be of : y= I3x-6I and y=2 times the square root of x-6

chriss · Answer

y=13x-61, the domain would be all real numbers, in other words, there is no restriction to what real numbers will produce a result for this problem

$$y=2\sqrt{x-6}$$

in this problem the restriction is that the radicand (x-6) has to be nonnegative.  that mean that x-6 has to be equal to or greater than 0, or in symbolic form
$$x-6\ge0$$
then solve for x
$$x \ge6$$
which is the answer to your question.  I don't know form your answer needs to take, but $$x \ge 6$$
should be sufficient to answer that question.  Although if specified you could also answer it in interval notation with$$(6,\infty)$$
or set notation of
$$\left\{ {x \in \mathbb{R}:xge6} \right\}$$

chriss · Answer

I just noticed in my earlier example I said the square root of x had to be nonnegative integers, that's not right, it has to be nonnegative real numbers.  Sorry for the error.

anonymous · Answer

thank you so much!

chriss · Answer

you're welcome :)