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Let f(x) = 3x - 4$ and g(x) = 3x + c$.  Find c if (f \circ g)(x) = (g \circ f)(x) for all x.

 Dec 22, 2023
 #1
avatar+126665 
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( f ° g) x = (g ° f) x

 

3(3x + c) - 4 = 3(3x - 4) + c

 

9x + 3c - 4 = 9x - 12 + c

 

3c - 4 = -12 + c

 

2c  =  -8

 

c = -8 / 2  =    -4

 

cool cool cool

 Dec 23, 2023

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