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October 1st, 2017, 12:26 PM   #1
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A consistent way to find range and domain?

Is there a consistent way to find range and domain to a function,
instead of relying on intuition?


For instance:

f(x) = sqr(x+2) / ln[abs(x)]

Last edited by duyht; October 1st, 2017 at 12:28 PM.
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October 1st, 2017, 12:57 PM   #2
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Domain is simple (with respect to real numbers)

no dividing by zero

no logs or square roots of negative numbers

no arguments to arcsin or arccos functions outside [-1,1]

Range is harder

you just have to look at where the function takes its domain.

There's no magic spell to do this, but once you have the domain nailed down it shouldn't be all that difficult unless it's a problem especially designed to be.

Last edited by skipjack; October 1st, 2017 at 06:24 PM.
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October 1st, 2017, 01:03 PM   #3
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Quote:
Originally Posted by duyht View Post
Is there a consistent way to find range and domain to a function,
instead of relying on intuition?


For instance:

f(x) = sqr(x+2) / ln[abs(x)]
applying my last post to this problem what do we get

$x\neq 0 \Rightarrow |x| > 0$

So as long as $x\neq 0,~|x|$ can be used as an argument to $\ln(x)$

No dividing by zero means $\ln(x) \neq 0$ i.e. $|x| \neq 1$, i.e. $x \neq -1,~1$

I assume you mean $\sqrt{x+2}$ in the numerator and this gets us $x \geq -2$

Combining all this we get

$x \geq -2,~x \neq -1,~x \neq 1,~x \neq 0$

i.e.

$x \in (-2,-1)\cup (-1,0) \cup (0,1) \cup (1,\infty)$

Figuring out the range of this function is much more difficult and I'll leave you to see where this function maps each part of the domain.
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October 1st, 2017, 01:21 PM   #4
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Quite frankly, the simplest way to find the range of a function is to graph it:
https://www.desmos.com/calculator/of3br6jkhx
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October 1st, 2017, 01:31 PM   #5
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Quote:
Originally Posted by Country Boy View Post
Quite frankly, the simplest way to find the range of a function is to graph it:
https://www.desmos.com/calculator/of3br6jkhx
but what if you are stranded in the desert and need to know the range of a function!
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October 1st, 2017, 04:46 PM   #6
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Well, yes, it happens to me all the time that I am stranded in the desert and need to find the range of a function in order to survive! That's why I always carry a computer with me when I go into the desert!
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