Confusion about the range of a function Watch

username1398367
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y=2x: y gets to 6 just as x gets to 3; intuitively, y has missed out half of the numbers; why is it correct to say that the range and the domain of the function are both \mathbb{R}

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Mr_Muffin_Man
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(Original post by dire wolf)
y=2x: y gets to 6 just as x gets to 3; intuitively, y has missed out half of the numbers; why is it correct to say that the range and the domain of the function are both \mathbb{R}

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R defines all the real numbers from negative infinity to positive infinity. The reason the range and domain are both R is because you can sub in any value for x as the domain and still get a number y as the range. I understand what you mean about y gets to 6 just as x gets to 3 but while x gets to 3, x could have possibly taken on the values of 2.5, 2.6, 2.7, 2.8888888 etc (That may not have been explained amazingly well but if you drew the graph of y=2x on a huge grid you'd see it could take on any possible value)

To summarise - there is no number you can sub in as your x value (domain) to get an invalid number for y (range)
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james22
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The domain is the values that x can take. In this case it makes sense for x to take any real value. The range is the values that y can take. Here y can take every possible real value. If A is a real number, then x=A/2 gives y=A.
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ghostwalker
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(Original post by dire wolf)
y=2x: y gets to 6 just as x gets to 3; intuitively, y has missed out half of the numbers; why is it correct to say that the range and the domain of the function are both \mathbb{R}

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Intuition can sometimes lead one astray.

The domain and range both contain an infinite number of values, and twice infinity (or half infinity) is still infinity. This topic is covered in first year uni. when talking about the cardinality of sets.

Look it up if you wish, but it's not something you're expected to know about at A-level, and may confuse rather than help.
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davros
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(Original post by ghostwalker)
Intuition can sometimes lead one astray.

The domain and range both contain an infinite number of values, and twice infinity (or half infinity) is still infinity. This topic is covered in first year uni. when talking about the cardinality of sets.

Look it up if you wish, but it's not something you're expected to know about at A-level, and may confuse rather than help.
It doesn't help that A level treats functions in such a poor way - the domain of a function should always be specified. If the function y = 2x were given with a domain of N instead of R then there would indeed be values that were never "hit".
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