Question

Can someone help me ?

I need to find the domain of the rational function below.

Answer 1

\[f(y)= \frac{ y + 1 }{ y^2 - y }\]

Answer 2

Here y can not be zero --(1)

Answer 3

\(\cfrac{y+1}{y(y-1)} = f(y)\)

Answer 4

The domain will be all valid y values - ie all values EXCEPT ones that cause the denominator to be zero, since that'll lead to dividing by zero.

The denominator, y(y-1)=0 will help find any y values NOT in the domain.

Answer 5

if y =1 then the denominator equals zero which we don't want!

Answer 6

So 1 and zero can not be the solutions

Answer 7

Would I just plug in a number and try and solve?

Answer 8

Well \(y(-1) =0\) equalize the denominator to zero.

find the solutions for y, and those will not include in the domain!

Answer 9

So I think the domain will bee any value except \(y \ne 0,1\) . @agent0smith check if I have some mistake!

Answer 10

Did you get it @angelina22309 ?

Answer 11

Correct @mathslover

@angelina22309 the domain will be all y values except for 0 and 1.

Answer 12

Its asking me to type my answer in interval notation, so if the domain is all y values except for 0 and 1, how would i write that?

Answer 13

R-{0,1}

Answer 14

erm... maybe something like... \[\large (-\inf, 0) \cup (0, 1) \cup (1, \inf)\] not 100% sure if that's the best/simplest way, but it should be valid. @mathslover's method might be more simple.

Answer 15

That is what i have
R - {0,1}

As R represents real number here .. and we have write it in "interval notation"

Answer 16

Isn't that set builder notation? http://www.regentsprep.org/Regents/math/ALGEBRA/AP1/IntervalNot.htm

Answer 17

Yeah.. you're right, sorry .. mistake

Answer 18

I need to refresh my knowledge

Answer 19

haha I had to google interval notation to remember that s#!t.

Answer 20

@angelina22309 maybe read http://www.regentsprep.org/Regents/math/ALGEBRA/AP1/IntervalNot.htm to get an idea of interval notation.