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 May 22nd, 2014, 10:38 AM #1 Newbie   Joined: May 2014 From: Na Posts: 1 Thanks: 0 Square Roots Can someone help me out here. What is the difference between -√(x-2)^2 and √(x-2)^2. I'm using khan academy to learn algebra 2 and this showed up on one of the problems to make a function inverse. Link to the problem itself below. https://www.khanacademy.org/math/alg...rses-example-3 May 22nd, 2014, 01:26 PM #2 Senior Member   Joined: Jul 2013 From: United Kingdom Posts: 471 Thanks: 40 Well there's a big difference between the two expressions. If x=3, $\displaystyle -\sqrt { { \left( 3-2 \right) }^{ 2 } } =-\sqrt { 1 } =-1$ $\displaystyle \sqrt { { \left( 3-2 \right) }^{ 2 } } =\sqrt { 1 } =1$ Take a look at this graph: https://www.desmos.com/calculator/qohzruuclo May 22nd, 2014, 02:04 PM #3 Senior Member   Joined: Jul 2013 From: United Kingdom Posts: 471 Thanks: 40 Ok... $\displaystyle f\left( x \right) =y={ \left( x-1 \right) }^{ 2 }-2\quad \{ x\le 1\} \\ \\ When\quad x=1,\quad y=-2\\ \\ When\quad x\rightarrow \infty ,\quad y\rightarrow \infty \quad \therefore \quad f\left( x \right) \ge -2\\ \\ Now...\\ \\ y={ \left( x-1 \right) }^{ 2 }-2\\ \\ { \left( x-1 \right) }^{ 2 }=y+2\\ \\ x-1=\pm \sqrt { y+2 } \\ \\ x=\pm \sqrt { y+2 } +1\\ \\ \therefore \quad f^{ -1 }\left( x \right) =\sqrt { x+2 } +1\quad or...\quad f^{ -1 }\left( x \right) =-\sqrt { x+2 } +1\\ \\ but\quad domain\quad of\quad f^{ -1 }\left( x \right) \quad is\quad \{ x\ge -2\} ,\quad and\quad f^{ -1 }\left( x \right) \le 1\\ \\ \sqrt { x+2 } +1\le 1\\ \\ \sqrt { x+2 } \le 0\\ \\ x+2\le 0\\ \\ x\le -2\quad but\quad domain\quad of\quad f^{ -1 }\left( x \right) \quad is\quad \{ x\ge -2\} \\ \\ \therefore \quad f^{ -1 }\left( x \right) =-\sqrt { x+2 } +1\quad \{ x\ge -2\} \quad f^{ -1 }\left( x \right) \le 1\\ \\$ Graph Demonstration: https://www.desmos.com/calculator/1vh56wxriv Tags roots, square Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post fe phi fo Elementary Math 4 May 13th, 2013 07:21 PM drewm Algebra 4 July 16th, 2011 08:35 PM drewm Algebra 3 July 16th, 2011 07:09 PM micheal2345 Algebra 11 November 8th, 2009 07:41 AM romeroom Algebra 7 March 17th, 2009 01:53 PM

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