Let f(x) = 2x + 7 and g(x) = 3x + c. Find c if \((f\circ g)(x)=(g\circ f)(x)\) for all x.
We need to solve this
f(g(x)) = g (f (x))
2(3x + c) + 7 = 3(2x + 7) + c simplify
6x + 2c + 7 = 6x + 21 + c subtract 6x from both sides
2c + 7 = 21 + c subtract c , 7 from both sides
c = 14
