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# Range of a function C3 Functions topic watch

1. Hi all!

Now I'm finding this question a little hard. The question is find the rangeof the function defined by f(x) = (2x-1)/(x-5) with the domain 6<x<8

I subbed in 6 and 8 into the function and got an answer of 5<f(x)<11. The answer in the back of my book is 0<f(x) < 2/3

A helping hand would be much appreciated! :-)
2. I'm pretty sure you're correct.

Have moved this over to maths.
3. you don't always get the biggest values of y at the ends of the domain...

if you have a graphical calculator you can plot the curve to see what happens.
4. (Original post by Kvothe the Arcane)
I'm pretty sure you're correct.

Have moved this over to maths.

And can I clarify, is the substitution method the easiest way to find the range? And does it work every time?
5. (Original post by Zarantulas)

And can I clarify, is the substitution method the easiest way to find the range? And does it work every time?
You need to sketch the graph. The bounds of your domain may not be the local maximum and minimum. Your graph is the same as and has asymptotes at and .

It looks like:

6. (Original post by Zarantulas)
Hi all!

Now I'm finding this question a little hard. The question is find the rangeof the function defined by f(x) = (2x-1)/(x-5) with the domain 6<x<8

I subbed in 6 and 8 into the function and got an answer of 5<f(x)<11. The answer in the back of my book is 0<f(x) < 2/3

A helping hand would be much appreciated! :-)
Can verify that the answer in the book is wrong. Though coming to your 'easiest way' point, it may not always be the case as such for a curve such that then subbing in these values will not give you the correct range.
7. (Original post by Kvothe the Arcane)
You need to sketch the graph. The bounds of your domain may not be the local maximum and minimum. Your graph is the same as and has asymptotes at and .

It looks like:

OK thank you! :-)

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