Given the question "If 9i is a root of the polynomial function f(x), which of the following must also be a root of f(x)?" The correct answer is -9i.
Given a polynomial with a complex root, then the conjugate of the complex root must also be a root to that polynomial function.
The conjugate of a complex number is the number with equal real part and imaginary part but with the sign between the real part and the imaginary part opposite. For example, the complex conjugate of 3 + 4i is 3 − 4i.
Therefore, given that 9i is a root to a polynomial function f(x), the conjugate of 9i = -9i will also be a root to the equation.
