Find the domain. 4/x-2. Please show all of your work and express your answer in interval notation.

Question

anonymous · Answer

I'll assume you mean $$4\div(x-2)$$ or "four over x minus two." The domain is any input for which the function is well defined. Remember that you cannot ever divide anything by zero, so the thing to look out for in quotients is any input value that will cause the function to try and divide something by zero; thus here, (x-2) cannot be equal to zero. So basically, the function is well defined for x at any real number other than two, or:

$$x \in(-\infty,2)\cup(2,\infty)$$

anonymous · Answer

Can you show me how you got that answer?

anonymous · Answer

$$(x-2)=0$$
$$x-2+2 = 0+2$$
$$x=2$$

anonymous · Answer

great! Thank you!