What is the range of the function (2\cos x)?
Answer and explanation
Correct answer: \([-2,2]\)
Since \(\cos x\) lies between \(-1\) and \(1\), multiplying by 2 gives values of \(2\cos x\) from \(-2\) to \(2\). The endpoints are included because \(2\cos 0=2\) and \(2\cos \pi=-2\). Thus, \([-1,1]\) is the range of \(\cos x\), not of \(2\cos x\). Exam tip: the range of \(a\cos x\) is \([-|a|,|a|]\).
Frequently asked questions
What is the correct answer to this question?
\([-2,2]\)
Why is this the correct answer?
Since \(\cos x\) lies between \(-1\) and \(1\), multiplying by 2 gives values of \(2\cos x\) from \(-2\) to \(2\). The endpoints are included because \(2\cos 0=2\) and \(2\cos \pi=-2\). Thus, \([-1,1]\) is the range of \(\cos x\), not of \(2\cos x\). Exam tip: the range of \(a\cos x\) is \([-|a|,|a|]\).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
