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If $f (x) = x + 2$ and $g (x) = x^2$, then for what value of $x$ does $f(g(x)) = g(f(x))$? Express your answer as a common fraction.

 Feb 9, 2019
 #1
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+1

-1/2

 Feb 9, 2019
 #2
avatar+104807 
+1

f(g(x))  =  x^2 + 2

g(f(x) )   =  (x + 2)^2

 

So.....we want to know

 

x^2 + 2  =  (x + 2)^2       simplify

 

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

 

2 = 4x + 4                      subtract  from both sides

 

-2 = 4x                       divide both sides by  4

 

-2 / 4 =   x =   - 1 /2

 

 

cool  cool  cool

 Feb 9, 2019

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