Question

Please help:)

Answer 1

So I had to simplify \[\frac{ 4x ^{2}+7-2 }{ 4x-1 }\]that part is done but now it's asking explain why f(1) = 3, f(0) = 2, and f(-1) = 1, yet f\[\frac{ 1 }{ 4 }\] is undefined.

Answer 2

well, if the denominator of a fraction is zero, then the number is undefined

Answer 3

just looking at the denominator

4x-1

what happens if x=1/4?

Answer 4

and i also assume its possible to cancel out the denominator, but that only works if what you're canceling out is equal to 1, not zero

Answer 5

so it would be like this?

4 (1/4) -1=1?

Answer 6

long story short
1/1= 1
0/0 is not 1

Answer 7

...
4 times 1/4 is?

Answer 8

in other words, 4 divided by 4 is?

Answer 9

1

Answer 10

ok now 1-1 is?

Answer 11

0 which the reason it is undefined correct?

Answer 12

ok now,
lets look at trends

1/1= 1

1/.1 =10

1/.01 =100

1/.001=1000

so lets assume 0 is equivalent to a really really low number, like .0000000000000000000000001

so what happens when we get
1/0
?

Answer 13

Undefined?

Answer 14

well, we get an infinitely large number

or as some would call it, infinity

but infinity is not an actual number, thus which is why we considered it undefined

Answer 15

so basically, if you ever get a fraction whose denominator is zero, then the solution is undefined


however, if you're dealing with limits, then its infinity

a third note 0/0 is not equal to 1

Answer 16

ok back to your previous question, do you think you can answer it now?

Answer 17

Maybe only for the reason why 1/4 is undefined but not the others. I don't understand why it's asking to explain why f(1) = 3, f(0) = 2, and f(-1) = 1

Answer 18

ok, so basically,
what you were asked to simplify, is what is being considered as a function
f(x)

so when x =1, then the fraction is equal to 3
when x-0, then the fraction is equal to 2

your question is asking, why do those values have actual answers, when x=1/4 does not

Answer 19

So pretty much it's like saying
4(1)-1=3
I don't get how
f(0)=2 and f(-1)=1

Answer 20

no, the function is the entire fraction, not just the denominator

Answer 21

f(0)= (4*0^2-7(0)-2)/(4(0)-1)=?

Answer 22

2 OH OKAY

Answer 23

I get it now:)Thank you very much!!