If the minimum value of f(x)=x^2+18x+a is the same as the minimum value of f(f(x)), what is the max value of a?

Answer 1

df/dx = 2x+18
dg/dx = (2f+18)(2x+18)

df/dx=0 when x = -9
dg/dx=0 when f = -9 or x = -9

f = -9 means
x^2+18x+a = -9
x = -9±√(72-a)

So, a <= 72