We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+1
179
3
avatar+814 

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
avatar
+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+100587 
+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+814 
+2

Thank you! Great!

 Aug 26, 2018

8 Online Users

avatar