Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Range of a function

What is the range of this function:

Thanks.

bossk171

Member

Registered: 2007-07-16

Posts: 305

Re: Range of a function

As x approaches 1 from the right, f(x) approaches infinity,  As x approaches infinity, f(x) approaches 0 so for x>1, f(x) > 0.

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mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Range of a function

First find the range of x²-1, given the same domain.
Then use that range as the domain of g(x)=1/x, and find the range of that function.

If I haven't made any mistakes,

Post collision aaaaa

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It wanted to be normal.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Range of a function

Sorry to bring this up again, but I want to make sure I understand it.

The range of h(x) using x>1 will give the domain of g(h(x)), and the range of g(h(x)) will be equal to the range of f(x)?

NullRoot

Member

Registered: 2007-11-19

Posts: 162

Re: Range of a function

Daniel

That sounds right. Just think of it this way:

1/(x²-1) is pretty much the same as 1/(some numbers). Once you work out the possibilities for the 'some numbers' then you should be able to analyze what possible values 1/(x²-1) can give you.

Here 'some numbers' is defined as x²-1, where x is any Real number greater than 1. So we know it can be anything from just over zero to as big as you want and that it increases continuously throughout.

So when you try the range of values from x²-1 you see 1/(a very small number) gives you a very large number. When you try 1/(a very large number) you get a small, positive number.

Last edited by NullRoot (2007-12-04 21:28:04)

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Trillian: Five to one against and falling. Four to one against and falling… Three to one, two, one. Probability factor of one to one. We have normality. I repeat, we have normality. Anything you still can’t cope with is therefore your own problem.

Khushboo

Member

Registered: 2007-10-16

Posts: 47

Re: Range of a function

Thats very right, so if the denominator is a very large number the value produced will be a small number. So when x approaches infinity, f(x) will approach 0.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Range of a function

that was a good explanation, thanks!