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February 15th, 2017, 12:50 PM   #1
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Question Help to clarify an issue with Injective function

Hey guys,

Can you help me, with how do I know if the following question is an Injective, surjective...etc function? since I have square root and both x1 and x2 are in minus sign, under the square root.

Also, when do I know when to reduce my range to R+, R-, R?

Thanks in advance!!


Last edited by shanytc; February 15th, 2017 at 12:53 PM.
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February 15th, 2017, 02:25 PM   #2
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What is the domain of f?
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February 15th, 2017, 02:49 PM   #3
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F(x) = Arccot(x/square root of (1-x squared))

Arccot: R -> (0, PI)

Domain is R
Range: 0,PI
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February 15th, 2017, 03:15 PM   #4
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The denominator can't be zero, so the domain can't be R.
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February 15th, 2017, 03:26 PM   #5
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Quote:
Originally Posted by skipjack View Post
The denominator can't be zero, so the domain can't be R.
Yes, I know that. I meant R for the definition of arccot.

My question is about the X1 = +-X2, if it narrows the domain even more.

Last edited by skipjack; February 15th, 2017 at 04:31 PM.
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February 15th, 2017, 05:03 PM   #6
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Okay, but I asked for the domain of f, not arccot.

Your equations imply that $x_1 = -x_2$ holds only when both are zero.
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February 16th, 2017, 11:08 AM   #7
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Quote:
Originally Posted by skipjack View Post
Okay, but I asked for the domain of f, not arccot.

Your equations imply that $x_1 = -x_2$ holds only when both are zero.
Wel, if the denominator can't be zero,
Than the domain must be R+ then.
No?
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February 16th, 2017, 03:24 PM   #8
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Don't you want the denominator to be real?
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