
Differential Equations Ordinary and Partial Differential Equations Math Forum 
 LinkBack  Thread Tools  Display Modes 
October 15th, 2017, 12:59 AM  #1 
Member Joined: Apr 2017 From: India Posts: 34 Thanks: 0  Functions
If y= arc cos((x^2)/2), then state the interval on which y is defined?

October 15th, 2017, 01:30 AM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,610 Thanks: 550 Math Focus: Yet to find out.  
October 15th, 2017, 05:52 AM  #3 
Math Team Joined: Jul 2011 From: Texas Posts: 2,761 Thanks: 1416 
$1 \le \dfrac{x^2}{2} \le 1$ $\dfrac{x^2}{2} \le 1 \implies x^2 \ge 2$, which is true for all $x \in \mathbb{R}$ $1 \le \dfrac{x^2}{2} \implies x^2 \le 2 \implies \sqrt{2} \le x \le \sqrt{2}$ intersection of the two solution sets is the latter ... $x \le \sqrt{2}$ Since $\dfrac{x^2}{2} \le 0$ for $x \le \sqrt{2}$, $\dfrac{\pi}{2} \le y \le \pi$ Last edited by skeeter; October 15th, 2017 at 06:17 AM. 

Tags 
differential, functions 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
functions  paul19  Calculus  5  November 21st, 2016 01:15 PM 
Derivatives, trignometric functions and exponential functions  Nij  Calculus  2  November 25th, 2015 06:20 AM 
Functions help  lamhmh  Applied Math  2  June 19th, 2011 09:59 PM 
Functions  hoyy1kolko  Algebra  1  January 7th, 2011 05:37 AM 
help / functions  sel  Calculus  3  October 21st, 2008 03:48 AM 