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.
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
