Question

Which inverse functions have a denominator involving \[|x|\sqrt{x^2-1}\]?

Options

• \[\sec^{-1}x\] and \[\operatorname{cosec}^{-1}x\]

• \[\sin^{-1}x\] and \[\operatorname{cosec}^{-1}x\]

• \[\sin^{-1}x\] and \[\cos^{-1}x\]

• \[\tan^{-1}x\] and \[\cot^{-1}x\]

Answer 1

The derivatives of \[\sec^{-1}x\] and \[\operatorname{cosec}^{-1}x\] involve \[|x|\sqrt{x^2-1}\]. Their stated domain restriction is \[|x|>1\].