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avatar+1791 

Let $f(x)$ and $g(x)$ be functions.   Find $c$ if
(f \circ g)(x) = (g \circ f)(x)
for all $x$, where $f(x) = 2x + 1$ and $g(x) = -3x + c$.

 Jan 13, 2024
 #1
avatar+128732 
+1

f(g(x))  =  2(-3x + c) + 1 =  -6x + 2c + 1

 

g(f(x))  =  -3(2x + 1) + c  = -6x -3 + c

 

f(g(x))  = g(f(x))

 

-6x + 2c + 1  = -6x - 3 + c         simplify as

 

c = -4

 

 

cool cool cool

 Jan 13, 2024

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