+0  
 
+1
77
1
avatar+544 

https://vle.mathswatch.co.uk/images/questions/question2239.png

lynx7  Feb 11, 2018
 #1
avatar+86935 
+2

f(g(x)  =  2 [x^2] + 1

 

g(f(x))  =  [ 2x + 1 ] ^2

 

So

 

f(g(x))  =  g (f (x) ) 

 

2 [ x^2]  + 1  =  [2x +  1 ] ^2

 

2x^2 + 1  =  4x^2 + 4x + 1      subtract  2x^2 , 1  from both sides

 

2x^2 + 4x  = 0      factor

 

2x ( x  + 2 )  = 0

 

Setting each factor to 0  abd solving for x produces  x = 0 , -2

 

 

cool cool cool

CPhill  Feb 11, 2018

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