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Class 12MathematicsInverse Trigonometric FunctionsIntroduction to inverse trigonometric functionsMedium
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On which interval is \(\cos^{-1}x\) a decreasing function?

Answer and explanation

Correct answer: \(\left[-1,1\right]\)

By making (\cos x) one-one on \(\left[0,\pi\right]\), \(\cos^{-1}x\) becomes decreasing on \(\left[-1,1\right]\). The graph direction also confirms this.

Related tags

Inverse-TrigonometryMonotonicityArccosIntroduction To Inverse Trigonometric FunctionsInverse Trigonometric FunctionsMathematicsClass 12 Mcq
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10 more MCQs
  1. 1What is the value of (\sin^{-1}1)?
  2. 2What is the principal value of \(\cot^{-1}0\)?
  3. 3Which of the following inverse trigonometric functions has all real numbers as its domain?
  4. 4If (y=\sin^{-1}x), what does it mean?
  5. 5If \(y=\cos^{-1}x\), which relation is correct?
  6. 6If \(y=\tan^{-1}x\), which of the following is true?
  7. 7What happens when \(x=2\) is used in \(\sin^{-1}x\)?
  8. 8Which of the following statements is correct about \(\tan^{-1}5\)?
  9. 9What is the principal value of \(\sec^{-1}\left(\frac{1}{2}\right)\) ?
  10. 10What type of function is (\sin^{-1}x)?
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