Question

Is the domain of y = 1/(x – 10) all real numbers.

Answer 1

what happens if x=10?

Answer 2

have another look at the equation

if x = 10 what happens to y?

Answer 3

y=0 right

Answer 4

no

write the equation in full, but put 10 where there is x

Answer 5

ya thats what i did

Answer 6

no you didn't
write it out, on paper at home - or type it here - but take care.

The answer is not y=0

\[y=\frac{ 1 }{ (x-10) }\]

x=10

this is a simpler version of the other question you are viewing - just look carefully

Answer 7

dude i keep getting zero

Answer 8

(x-10)

x=10

x-10 = 0

1/(x-10) = 1/0

what is 1/0?

Answer 9

0

Answer 10

right???

Answer 11

OK this is wher the fundamental concept lies - and why you are not getting the answer to these questions.

1/0 is not 0

it is undefined - you cannot divide by 0 - it results in an infinite number - and is therefore undefined.

Therefore in any equation which has a fraction in it (such as the one in this question) the value of y is not defined when the denominator is zero

In this case the denominator is zero when x = 10.

But 10 is a real number, and results in an undefined value for y

therefore you should be able to answer "is y defined for all real numbers"? That is the answer to this question.

Answer 12

THANK YOU!

Answer 13

Just to repeat, we do *not* allow "divide by zero". So we exclude any numbers that cause that catastrophe. In this case, we do not allow x to be 10. we say the domain (allowed x's) is all real numbers *except* x=10