Given the function f (x) = (1 / 3) x cube - (A-1) x square + b square x, where a B is a real constant, a necessary and sufficient condition for the function f (x) to be an odd function is obtained

Given the function f (x) = (1 / 3) x cube - (A-1) x square + b square x, where a B is a real constant, a necessary and sufficient condition for the function f (x) to be an odd function is obtained

Because it is an odd function, it must have f (0) = 0, that is, B = 0 test has f (- x) = - f (x), so its sufficient and necessary condition is b = 0