Which of the following sets is the range of the function \(f(x)=3+\left(\dfrac{x^2-5x+6}{x^2+5x-6}\right)^2\) ?

\((0,3) \)

\([0,\infty) \)

\( (-\infty,\infty) \)

\( [-3,\infty) \)

\( [3,\infty)\)

Approach

Squared values cannot be negative, so the minimum value of \(f(x)\) is 3. All of the answer choices show minimum values lower than \(3\), which is not possible.