
PreCalculus PreCalculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
June 11th, 2017, 01:25 PM  #1 
Newbie Joined: May 2017 From: antartica Posts: 11 Thanks: 0  finding domain of square root function
State the domain of the following function using interval notation. sqrt( x^2 +10x 21) I got this answer (infinity, 5sqrt(46)] U [sqrt(46) 5, infinity) but it can't even be inputted in the answer part the answer part is as follows,(________,________) so I am not sure what to do. 
June 11th, 2017, 01:55 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,448 Thanks: 565 
The zeros of the function are $\displaystyle \sqrt{3}\ and\ \sqrt{7}$. The domain is that interval, since function is imaginary outside.

June 11th, 2017, 01:56 PM  #3  
Senior Member Joined: Sep 2015 From: USA Posts: 1,785 Thanks: 920  Quote:
$x^2  10x + 21 \leq 0$ $(x7)(x3) \leq 0$ $(x7)\leq 0 \wedge (x3)\geq 0 \bigvee (x7)\geq 0 \wedge (x3)\leq 0$ $x\leq 7 \wedge x\geq 3 \bigvee x \geq 7 \wedge x \leq 3$ the right hand condition is the empty set leaving $x \in [3, 7]$  
June 11th, 2017, 02:37 PM  #4 
Newbie Joined: May 2017 From: antartica Posts: 11 Thanks: 0 
That was correct thank you. I am still wondering though how you ignored the square root. the roots are 3 and 7 but what about thw square root do you just ignore it or...

June 11th, 2017, 02:53 PM  #5  
Math Team Joined: Jul 2011 From: Texas Posts: 2,722 Thanks: 1376  Quote:
$x^2+10x21 \ge 0$ ... as written by romsek. The values of x in the interval [3,7] satisfy this requirement ... all other values of x make the quadratic expression negative.  
June 11th, 2017, 02:59 PM  #6  
Newbie Joined: May 2017 From: antartica Posts: 11 Thanks: 0  Quote:
 

Tags 
domain, finding, function, root, square 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Sos need help with square root function  catmurr  Calculus  6  February 2nd, 2017 01:40 AM 
is a square root a function or not confusion  taylor_1989_2012  PreCalculus  6  September 27th, 2016 10:44 AM 
Square root function and quadratic function  hhmathgeek  Algebra  3  April 25th, 2016 03:38 PM 
SURD  Finding square root  sachinrajsharma  Algebra  15  February 23rd, 2013 06:51 PM 
Finding solution of square root differential equation  too_old  Differential Equations  1  December 5th, 2010 12:27 PM 