
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
June 27th, 2019, 01:13 PM  #1 
Newbie Joined: May 2018 From: United States Posts: 7 Thanks: 0 Math Focus: Algebra  Radical in Function
So I have solved the following problem, but I don't understand the underpinning "why" of a particular part. I am speaking of part a. in the problem We have function f composed of function g, which will look like this after plugging g(x) into f(x). I know (or at least I'm pretty sure) that my radical would simplify in the next step to $\displaystyle 7x+6$ if I weren't dealing with a function, and I was told no other specifics about what could or could not be inside the radical. The index of the radical is even, the power it is raised to is even, and the result is odd. The book tells me not to use absolute value however when removing the binomial from the radical, but rather just parentheses. Now I know that I am dealing with a function's radical, and the domains of radicals exclude imaginary numbers produced by negative values inside of radicals, but I don't quite see the reasoning here. Assuming I am on the right course of reasoning, can someone connect the dots for me? As far as I'm concerned, I'm not solving for the domain of the radical in that particular step, so I don't see why the way that I pull the value inside the radical to the outside should be affected by it. Last edited by skipjack; June 27th, 2019 at 05:07 PM. 
June 27th, 2019, 01:42 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,786 Thanks: 708 
If $x\le 7$, then $\sqrt{7x}$ is real and the square $7x\ge 0$. If $x\gt 7$, then $\sqrt{7x}$ is imaginary and the square $7x\lt 0$. 

Tags 
function, radical 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Radical equation  App  Algebra  2  April 1st, 2015 11:59 PM 
Radical  tallbabe1  Algebra  6  December 14th, 2012 06:41 PM 
Third derivative of radical function  henoshaile  Calculus  2  October 8th, 2012 11:02 AM 
Radical  mathkid  Calculus  4  September 28th, 2012 12:04 PM 
Jacobson radical and prime radical , please helpppp  peteryellow  Abstract Algebra  0  August 28th, 2008 04:10 AM 