[otrivine]

hi for this question
g:x- x/x-2 x>2

what is the range i am getting g(x)>3 ? correct or not thanks

[sputum]

not correct (assuming you meant x/(x-2) for x>2)
what happens when x gets very large?

[otrivine]

(Original post by sputum)
not correct (assuming you meant x/(x-2) for x>2)
what happens when x gets very large?

the y value increases

[sputum]

(Original post by otrivine)
the y value increases

3/(3-2) = 3
4/(4-2) = 2
5/(5-2) = 5/3
the function value decreases as x increases.

[otrivine]

(Original post by sputum)
3/(3-2) = 3
4/(4-2) = 2
5/(5-2) = 5/3
the function value decreases as x increases.

yes thats what i done but how would i convert it to the form of < > ??

[mr tim]

(Original post by otrivine)
yes thats what i done but how would i convert it to the form of < > ??

try using bigger numbers for x values like 100, 1000 etc. What is the y value getting towards?

[sputum]

(Original post by otrivine)
yes thats what i done but how would i convert it to the form of < > ??

How did you get

g(x)>3

?

Basically you look at the ends. Values very near the minimum (2) and the maximum (squillions+)
so for some small bit over 2 (say 15/7) you get (15/7)/(1/7) = 15. You can get to any positive number by taking a point near enough to x=2.
As the difference between a squillion and (squillion-2) is tiny, dividing one by the other gets you very close to 1. Ever-closer with larger values of n.
So you can't get to one (because n-2 just doesn't equal n) but you can hit anything over 1 and as vast as you like.

[otrivine]

(Original post by mr tim)
try using bigger numbers for x values like 100, 1000 etc. What is the y value getting towards?

look the values for x>2 then is like x=3,4,5 i can chose and when i sub in i get the values for y those are the ranges so then how can i convert it to <> thats what i want to know?

[otrivine]

(Original post by sputum)
How did you get ?

Basically you look at the ends. Values very near the minimum (2) and the maximum (squillions+)
so for some small bit over 2 (say 15/7) you get (15/7)/(1/7) = 15. You can get to any positive number by taking a point near enough to x=2.
As the difference between a squillion and (squillion-2) is tiny, dividing one by the other gets you very close to 1. Ever-closer with larger values of n.
So you can't get to one (because n-2 just doesn't equal n) but you can hit anything over 1 and as vast as you like.

look the values for x>2 then is like x=3,4,5 i can chose and when i sub in i get the values for y those are the ranges so then how can i convert it to <> thats what i want to know?

[TenOfThem]

When x is just over 2 e.g. 2.00000000001 what is the number like

When x is very big is there much difference between x and x-2 if there were no difference between them .... what number would you have

[sputum]

(Original post by otrivine)
look the values for x>2 then is like x=3,4,5 i can chose and when i sub in i get the values for y those are the ranges so then how can i convert it to <> thats what i want to know?

Well you can 'get' anywhere between 1 (excluding 1 itself as above) and as large a number as you can care to name (taking x as near to 2 as you like)
So the range of g(x) is >1 or (1,inf)
I don't know how this is taught at sixth form or how rigorous your answer needs to be.

[raheem94]

(Original post by otrivine)
hi for this question
g:x- x/x-2 x>2

what is the range i am getting g(x)>3 ? correct or not thanks

Now it is easier to deduce the range.

[otrivine]

(Original post by raheem94)


Now it is easier to deduce the range.

hi raheem how are you? ok my question is you know in the question they put x>2 right and that means i can chose any values greater than 2 like 3,4,5 and i sub in to equation and get the values and i will get the range values so which value should i use dont i use the one i sub in 3 to the equation cause that is the minimum value?many thanks

[mr tim]

(Original post by otrivine)
hi raheem how are you? ok my question is you know in the question they put x>2 right and that means i can chose any values greater than 2 like 3,4,5 and i sub in to equation and get the values and i will get the range values so which value should i use dont i use the one i sub in 3 to the equation cause that is the minimum value?many thanks

remember you use values of x>2 and that includes all REAL numbers (ie: 2,3,4 as well as 2.0000000000001) and because its any number more than 2 you have to use bigger numbers too like 100, 1000 etc. Try to use smaller numbers and bigger numbers and see what range you get.

[raheem94]

(Original post by otrivine)
hi raheem how are you? ok my question is you know in the question they put x>2 right and that means i can chose any values greater than 2 like 3,4,5 and i sub in to equation and get the values and i will get the range values so which value should i use dont i use the one i sub in 3 to the equation cause that is the minimum value?many thanks

I am fine.

The equation is

If we sub in x=3, we get, g(x)=3
If we sub in x=4 we get, g(x)=2
If we sub in x=5 we get, g(x) = 1.66666666666
...
If we sub in x=100 we get, g(x)=1.020408163
...
If we sub in x=1000 we get, g(x)=1.002004008
From above we can deduce that no value will be less than or equal to 1.

X=3 is not the minimum value for domain of x>2.

Now sub in x=2.01, we get, g(x)=201
...
Now sub in x=2.000001, we get, g(x)=2000001

This shows us that the range is g(x)>1.

Do you understand it now?

[otrivine]

(Original post by raheem94)
I am fine.

The equation is

If we sub in x=3, we get, g(x)=3
If we sub in x=4 we get, g(x)=2
If we sub in x=5 we get, g(x) = 1.66666666666
...
If we sub in x=100 we get, g(x)=1.020408163
...
If we sub in x=1000 we get, g(x)=1.002004008
From above we can deduce that no value will be less than or equal to 1.

X=3 is not the minimum value for domain of x>2.

Now sub in x=2.01, we get, g(x)=201
...
Now sub in x=2.000001, we get, g(x)=2000001

This shows us that the range is g(x)>1.

Do you understand it now?

so does it always have to be 1?

[raheem94]

(Original post by otrivine)
so does it always have to be 1?

It can't equal 1, it will be greater than 1.

[otrivine]

(Original post by raheem94)
It can't equal 1, it will be greater than 1.

yes so for any other equations should it always be greater than 1?

[raheem94]

(Original post by otrivine)
yes so for any other equations should it always be greater than 1?

No, it depends upon the question.

e.g. Range of the function will be

[otrivine]

(Original post by raheem94)
No, it depends upon the question.

e.g. Range of the function will be

thanks and how would u differentiate this
PEpower-KT ?