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If \(g(x)=\sqrt[3]{\frac{x+3}{4}}\), for what value of x will g(2x)=2(g(x))? Express your answer in simplest form.

 Aug 26, 2018
 #1
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+2

\(g(2x)=\sqrt[3]{\frac{2x+3}{4}}\)

\(2g(x)=2*\sqrt[3]{\frac{x+3}{4}}\)

Cubing both sides, we get \(\frac{2x+3}{4}=2x+6\)

Multiplying by 4, we get \(2x+3=8x+24\)

So \(x=-3.5\)\(\)

.
 Aug 26, 2018
 #2
avatar+98091 
+3

g (2x)  =  3√ [  (2x + 3) / 4 ]    (1)  

2 (g(x) ) =  2 * 3 √  [ (x + 3 ) / 4 ]    (2)

 

Let  us  cube  (1) , (2)  and set them equal...so we have...

 

(2x + 3) / 4  =  8 (x + 3) / 4

 

(2x + 3)  = 8(x + 3)

2x +  3  = 8x + 24

-21  = 6x

x  = -21/6  =  -7/2

 

 

cool cool cool

 Aug 26, 2018
 #3
avatar+809 
+2

Thank you! Great!

 Aug 26, 2018

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