My Math Forum Function :- Domain Range Problem

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 May 25th, 2019, 06:43 AM #1 Member   Joined: Jul 2017 From: KOLKATA Posts: 50 Thanks: 3 Function :- Domain Range Problem Let f :R --> [1,∞) be defined as f(x) = log⁡(√(x^2 - 4x + K + 1) + 10) and if f(x) is surjective, then K is Last edited by skipjack; May 25th, 2019 at 11:29 AM.
 May 25th, 2019, 07:20 AM #2 Member   Joined: Jul 2017 From: KOLKATA Posts: 50 Thanks: 3 My answer has come k > 1/3 . Is it correct ?
 May 25th, 2019, 11:27 AM #3 Global Moderator   Joined: Dec 2006 Posts: 21,027 Thanks: 2258 It's incorrect. Thanks from topsquark
 May 25th, 2019, 12:51 PM #4 Global Moderator   Joined: May 2007 Posts: 6,834 Thanks: 733 $x^2-4x$ has a minimum ($-4$) at $x=2$, so to keep the square root argument non-negative you need $k\ge 3$. Thanks from topsquark

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