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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: 17,919 Thanks: 1386 
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 (1x squared)) Arccot: R > (0, PI) Domain is R Range: 0,PI 
February 15th, 2017, 02:15 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 17,919 Thanks: 1386 
The denominator can't be zero, so the domain can't be R.

February 15th, 2017, 02:26 PM  #5 
Newbie Joined: Jul 2016 From: Israel Posts: 24 Thanks: 0  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: 17,919 Thanks: 1386 
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 
Newbie Joined: Jul 2016 From: Israel Posts: 24 Thanks: 0  
February 16th, 2017, 02:24 PM  #8 
Global Moderator Joined: Dec 2006 Posts: 17,919 Thanks: 1386 
Don't you want the denominator to be real?


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clarify, function, injective, issue 
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