My Math Forum  

Go Back   My Math Forum > High School Math Forum > Pre-Calculus

Pre-Calculus Pre-Calculus Math Forum


Thanks Tree6Thanks
Reply
 
LinkBack Thread Tools Display Modes
April 20th, 2019, 08:32 PM   #11
Senior Member
 
Joined: Aug 2012

Posts: 2,306
Thanks: 706

Quote:
Originally Posted by Pasta View Post
Right, thanks, and same applies to the other situations i mentioned right? (even power with even root if the result is an odd power)

No he's right @Maschke
No, he's wrong.

What is $\sqrt{(-4)^2}$? It's $4$.

It is true that if $f(x) = x^2$ then $f^{-1}(16) = \{-4, 4\}$. In this case $f$ does not have a functional inverse so the notation $f^{-1}$refers to the set inverse. This is the notation and the way you would think about it.

[I hope my terminology is clear. The functional inverse of $f$ is a function $g$ such that $fg = gf = id$ where the concatenation of functions refers to function composition. $fg$ means first $g$ and then $f$; and $id$ is the identity function on fhe reals. And the set inverse of a number is the set of values that are mapped to it by $f$].

If $x$ is a real variable the symbol '$\sqrt{}$' is defined to be the positive of the two values given by the set inverse. That's what the notation means. It does not mean anything else. It does not mean the set inverse. It doesn't mean "really one thing but we say it's another." The ONLY thing it means is the positive of the two values given by the set inverse.

If the variable $z$ is a complex number, we do not typically use the notation $\sqrt z$ because there is no notion of positive and negative numbers in the complex plane. We can of course choose a branch of a multi-valued complex function. But we never use the square root sign.

$\sqrt{x^2} = |x|$ and there is simply no other way to think about it that doesn't lead to confusion. If you want the set inverse, then write $f^{-1}(16) = \{-4, 4\}$.
Thanks from Joppy, SDK and Greens

Last edited by Maschke; April 20th, 2019 at 09:10 PM.
Maschke is offline  
 
April 21st, 2019, 12:03 AM   #12
Senior Member
 
Joined: Oct 2009

Posts: 782
Thanks: 280

Quote:
Originally Posted by Pasta View Post
No he's right @Maschke
He's very wrong.
Thanks from Maschke and SDK
Micrm@ss is offline  
April 21st, 2019, 10:10 AM   #13
Newbie
 
Joined: Apr 2019
From: Jor

Posts: 5
Thanks: 0

I'm not really into this advanced branch of math but for me, when he said √x² = |x| that seemed fine for me, maybe I didn't get what he really meant but whatever, I'm here for my basic question. in all the types of rational powers , when is it needed to use absolute values? or is sqrt(x^2) the only case?
Pasta is offline  
Reply

  My Math Forum > High School Math Forum > Pre-Calculus

Tags
absolute, radicals, radicsls



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Find the absolute minimum and absolute maximum. corleoneee Calculus 5 October 22nd, 2013 12:31 AM
Absolute Value Inequality with Absolute Values on Both Sides shiseonji Algebra 2 September 24th, 2013 08:36 AM
Converting radicals to mixed radicals with fractions ohaider Algebra 6 February 6th, 2012 07:13 PM
Help with radicals jonquil Algebra 6 April 13th, 2011 03:40 PM
Radicals Mr_Quick Algebra 3 May 14th, 2009 07:50 AM





Copyright © 2019 My Math Forum. All rights reserved.