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Let f and g be functions defined by f(x) =9x + 1 and g(x) = x^2.  Find all values of x that staisfy f(g(x)) = g(f(x)).

 Dec 10, 2019
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f(g(x)  = 9(x^2) + 1

 

g(f(x))  = (9x +1)^2

 

So  we have

 

(9x + 1)^2  = 9(x^2) + 1     simplify

 

81x^2 + 18x + 1   =  9x^2 + 1

 

72x^2  + 18x  = 0       factor

 

18x (4 x + 1 )  =   0

 

Set each factor to 0 and solve for  x   and we get that  x  = 0   and x  =  -1/ 4

 

 

cool cool cool

 Dec 10, 2019

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