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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.

 Oct 28, 2019
 #1
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g(2x)  =   [ (2x + 3)/ 4]^(1/3)

2g(x)  = 2 [ (x + 3) / 4] ^(1/3)

 

So.....we have that

 

[ (2x + 3)/4]^(1/3)  =  2[ (x + 3)/4]^(1/3)         cube both sides

 

(2x + 3)/4     =  8 (x + 3)/4

 

2x + 3   =  8(x + 3)

 

2x + 3  =  8x + 24

 

-6x = 21

 

x  = -21/6

 

x = -7/2

 

 

cool cool cool

 Oct 28, 2019

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