Question

Simplify f(x)=(3x^2-4x+1)/(3x-1)Using complete sentences, explain why f(1) = 0, f(0) = –1, and f(–1)=–2, yet f( 1/3 ) is undefined. Make sure to
show your work.

Answer 1

@myko ??? Can you help??

Answer 2

\(\frac{(3x^2-4x+1)}{(3x-1)}=\frac{(3x-1)(x-1)}{(3x-1)}=x-1\)
so : f(1) = 0, f(0) = –1, and f(–1)=–2
and f( 1/3 ) is not alowed , because it makes denominator in the original expretion 0

Answer 3

Okay so because it's 0 it's undefined? What should I say about why the f(1)=0 and f(0)=-1?

Answer 4

Does that also mean it's a restriction?

Answer 5

you function f(x)=(3x^2-4x+1)/(3x-1) was simplified to f(x)=x-1. So:
f(1)=1-1=0
f(0)=0-1=-1
and x=1/3 is not alowed, so it's a restriction

Answer 6

THANKS @myko !!!!! :D

Answer 7

Do you understand why division by 0 is undefined?

Answer 8

yw

Answer 9

When it equals 0 it means it's undefined

Answer 10

Yes that is true, but do you know why?

Answer 11

No why?

Answer 12

In math when we say something is undefined we mean that it is not part of the definition. In the case of division using 0 as a denominator is strictly not allowed.

Answer 13

if \(\huge \frac{a}{0}=b\) then it should be \(\huge b*0=a\). But here is no number \(\huge b\) that multiplied by \(\huge 0\) gives \(\huge a\), because any number multiplied by 0 equals 0

Answer 14

@skullpatrol

Answer 15

that's why

Answer 16

Ok gothcha! Thanks guys!! :) :)

Answer 17

np :)

Answer 18

@myko Your "proof" assumes that "IF a/0 =b then..." but using 0 in the denominator is strictly not allowed by the definition of division itself.

Answer 19

my proof says "In case a/0=b then ...". In other words, " supose a/0=b, then ..." . And you get to imposible situation, so the initial asumption have to be wrong

Answer 20

@skullpatrol

Answer 21

But this case is not allowed by the very definition of division.

Answer 22

that's what I prooved, because división is defind as a*(1/b) = a/b

Answer 23

Division is defined as a/b= a*(1/b) ; b=/=0

note: b=/=0 is IN the definition.

Answer 24

That is why using 0 for b is UNdefined by the definition.

Answer 25

read this http://en.wikipedia.org/wiki/Division_by_zero

Answer 26

I have read that.

Answer 27

so, if you agree with that, we are set, :)

Answer 28

I'm not saying I disagree.
I'm saying it is a matter of definition.