+0  
 
-1
82
1
avatar+851 

What is the smallest real number $x$ in the domain of the function $$\(g(x) = \sqrt{(x-3)^2-(x-8)^2}~?\)$$

Lightning  Jul 24, 2018
 #1
avatar+92430 
+1

√ [ (x - 3)^2  - (x - 8)^2 ]

 

As small as the expression under the radical  can be  is  0

 

So....setting it to 0, we have

 

(x - 3)^2  - (x - 8)^2   =  0 

Factor as a difference  of squares

 

[ (x - 3) + ( x - 8)] [ (x - 3) - ( x - 8) ]  = 0

 

Settting the second factor to 0  and solving for  x will not produce a solution

Setting the  first factor to 0 and solving for x  produces

 

( x - 3) + ( x - 8)  = 0

2x - 11  = 0

x  = 11/2 

 

So....the smallest x value in the domain is  x  = 11/2

 

Here's a graph that confirms this : https://www.desmos.com/calculator/qegganaegs

 

 

cool cool cool

CPhill  Jul 24, 2018

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