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)).
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
