What is the range of the function (2-4\cos^2 x)?

Correct answer: \([-2,2]\)

Since \(0\leq \cos^2 x\leq 1\), we get \(0\leq 4\cos^2 x\leq 4\). Hence, \(2-4\cos^2 x\) has minimum value \(-2\) when \(\cos^2 x=1\), and maximum value \(2\) when \(\cos^2 x=0\). Therefore, its range is \([-2,2]\). The interval \([0,2]\) is incorrect because the function can also take the value \(-2\). Exam tip: for an expression involving \(\cos^2 x\), first use its range \([0,1]\) and then test the endpoint values.