Question

The range of the function \(f(x) = (1 + {\sec ^{ - 1}}x)(1 + {\cos ^{ - 1}}x)\) is
1. \(\left( { - \infty ,\infty } \right)\)
2. \(\left( { - \infty ,0} \right] \cup \left[ {4,\infty } \right)\)
3. \(\left\{ {1,{{(1 + \pi )}^2}} \right\}\)
4. \(\left\{ {0,(1 + {\pi ^2})} \right\}\)

Answer 1

Correct Answer - Option 3 : \(\left\{ {1,{{(1 + \pi )}^2}} \right\}\)

Domain of f(x) is \(\left\{ {1, - 1} \right\}\) so range will be f(1) & f(–1).