May 20th, 2019, 01:12 AM  #1 
Member Joined: Jul 2017 From: KOLKATA Posts: 43 Thanks: 2  Function : Range Problem
If f(x) = pi( ( (sqrt(x7)) 4)/((x9)) then the range of y= sin( 2f(x)) is

May 20th, 2019, 05:00 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,746 Thanks: 2133  
May 20th, 2019, 07:59 AM  #3 
Member Joined: Jul 2017 From: KOLKATA Posts: 43 Thanks: 2 
Please refer to Question # 2 of the attachment

May 20th, 2019, 01:41 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,763 Thanks: 697 
Try to express your question more clearly  use LaTex.

May 20th, 2019, 01:54 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,746 Thanks: 2133  
May 20th, 2019, 02:31 PM  #6 
Math Team Joined: Jul 2011 From: Texas Posts: 2,940 Thanks: 1545 
note ... $\pi \left[\dfrac{\sqrt{x+7}4}{x9}\right] = \dfrac{\pi}{\sqrt{x+7}+4}$ $y = \sin\left(\dfrac{2\pi}{\sqrt{x+7}+4}\right)$ $x \in [7,\infty) \implies y \in \{?\}$ 
May 21st, 2019, 12:24 AM  #7 
Member Joined: Jul 2017 From: KOLKATA Posts: 43 Thanks: 2 
Many Thanks. Got it . So range of y should be (0,1] Right?

May 21st, 2019, 03:06 AM  #8 
Global Moderator Joined: Dec 2006 Posts: 20,746 Thanks: 2133 
No. As x = 9 isn't in the domain, 1/√2 isn't in the range.

May 21st, 2019, 12:43 PM  #9 
Global Moderator Joined: May 2007 Posts: 6,763 Thanks: 697  
May 21st, 2019, 03:40 PM  #10 
Math Team Joined: Jul 2011 From: Texas Posts: 2,940 Thanks: 1545  

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