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January 8th, 2014, 03:42 AM   #1
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How do I find the image set and domain?

Hi all, wondered if anyone could point me in the right direction.

I am given a function f(x)=-3(x-1)^2+12 (where x is less than or equal to 1 and less than or equal to 3)

and asked to find the domain and image set of the inverse function f^-1.

Trouble is there was only a small paragraph on image sets in the text book and I can't see what it is all about so have no clue how one goes about it!
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January 8th, 2014, 05:16 AM   #2
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Re: How do I find the image set and domain?

http://en.wikipedia.org/wiki/Image_%28mathematics%29

Try this to start. There will be loads more stuff online as well.
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January 8th, 2014, 05:51 AM   #3
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Re: How do I find the image set and domain?

Wikipedia can be a bit too mathematical sometimes, especially when you just want a simple explanation.

Given a function f, then the input of f is the domain of f, and the output of f is the image set of f.

For example:



The domain of this funtion, ie. the range of numbers you can use as x, is

But it will never output a negative number so its image set, the range of numbers that come out of f, is

Generally, the domain of a function is the image set of the inverse of the function, and the image set of a function is the domain of the inverse of the function.

However, you have to be wary of apparent functions that fail the horizontal (or vertical) test as their inverse is not a true function.
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