f(x) = 5 / (x - 2) answer: x ≠ 2 My lesson does not tell me how they got that answer. I can not figure it out.

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f(x) = 5 / (x - 2) answer: x ≠ 2 My lesson does not tell me how they got that answer. I can not figure it out.

Mathematics
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What do you think is the value of f(x) when x=2, or in short, what is f(2)?
if x = 2 then it would be f(x)= 5/0 which is just f(x) = 5?
Nope, division by 0 is not defined so \[\frac{5}{0}\] has no meaning, that's why x can take any value except 2 This is also the reason why you can't multiply both sides of an equation by 0 consider \[y=2x\] If you multiply both sides by 0 you get \[y \times 0=2x \times 0\] Now one may say to get back the original equation we simply have to divide by 0 \[\frac{y \times 0}{0}=\frac{2x \times 0}{0}\] Now division by 0 is not defined, so this has no meaning, so you just simply can't multiply both sides of an equation by 0

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Also remember \[\frac{5}{1}=5\] and you are saying \[\frac{5}{0}=5\] This implies that \[1=0\] which is not true
okay so since division by 0 is not defined, it would give x an infinite amount of values other than 2 because of how we worked out the equation? like x - 2 = 0 turns into x = 2 and when x is replaced by 2 we get 0 which brings us back to it being undefined?
Yes and this is what we call the "domain" of the function, the set of all the values that x can take symbolically we write |dw:1441558284235:dw| Set of real numbers minus the set containing number 2
Basically x can take any value except 2 because for 2 it is not defined
thank you!!!

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