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 February 15th, 2017, 11:50 AM #1 Newbie   Joined: Jul 2016 From: Israel Posts: 24 Thanks: 0 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 11:53 AM.
 February 15th, 2017, 01:25 PM #2 Global Moderator   Joined: Dec 2006 Posts: 18,951 Thanks: 1599 What is the domain of f?
 February 15th, 2017, 01:49 PM #3 Newbie   Joined: Jul 2016 From: Israel Posts: 24 Thanks: 0 F(x) = Arccot(x/square root of (1-x squared)) Arccot: R -> (0, PI) Domain is R Range: 0,PI
 February 15th, 2017, 02:15 PM #4 Global Moderator   Joined: Dec 2006 Posts: 18,951 Thanks: 1599 The denominator can't be zero, so the domain can't be R.
February 15th, 2017, 02:26 PM   #5
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Quote:
 Originally Posted by skipjack 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 03:31 PM.

 February 15th, 2017, 04:03 PM #6 Global Moderator   Joined: Dec 2006 Posts: 18,951 Thanks: 1599 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.
February 16th, 2017, 10:08 AM   #7
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Quote:
 Originally Posted by skipjack 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?

 February 16th, 2017, 02:24 PM #8 Global Moderator   Joined: Dec 2006 Posts: 18,951 Thanks: 1599 Don't you want the denominator to be real?

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