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TIA!

find formula for the inverse of the function 

sqrt x^2+8x, x>0 

 Mar 4, 2019
 #1
avatar+100546 
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I'm assuming that we have

 

y = √[x^2 + 8x ]       square both sides

 

y^2 =  x^2 + 8x        complete the square on x

 

y^2 =     x^2 + 8x + 16  - 16   factor

 

y^2 = ( x + 4)^2  - 16      add 16 to both sides

 

y^2 + 16 =  (x + 4)^2      take the positive root

 

√[ y^2 + 16 ] = x + 4       subtract 4 from both sides

 

√[ y^2 + 16] - 4 = x       swap x and y

 

√ [ x^2 + 16 ] - 4 = y   = the inverse    [ where x is also > 0 ]

 

coolcool cool

 Mar 4, 2019

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