May 25th, 2019, 06:43 AM  #1 
Member Joined: Jul 2017 From: KOLKATA Posts: 43 Thanks: 2  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: 43 Thanks: 2 
My answer has come k > 1/3 . Is it correct ?

May 25th, 2019, 11:27 AM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,746 Thanks: 2133 
It's incorrect.

May 25th, 2019, 12:51 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,763 Thanks: 697 
$x^24x$ has a minimum ($4$) at $x=2$, so to keep the square root argument nonnegative you need $k\ge 3$.


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domain, function, problem, range 
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