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  • Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.4 Question 3 Subquestion (i) Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Inverse Trigonometric Function Exercise 3.4 Question 3 Subquestion (i) Maths Textbook Solution.

Answers (1)

Answer: \left (-\infty,0\right ] \cup \left [ \frac{2}{3},\infty \right )
Hint: Domain \left ( y^{-1} \right )= Range\left ( y \right )
Domain of \sec ^{-1}\left ( x \right )=\left ( -\infty,-1 \right ]or\left [ 1,\infty \right ]
Given:    \sec ^{-1}\left ( 3x-1 \right )
Solution: We know that the range of   \sec x\, is \left ( -\infty,-1 \right )\cup \left ( 1,\infty \right )
3x-1< -1\: and \: 3x-1\geq 1
3x< -1+1\: and \: 3x\geq 1+1
3x< 0 \: and\: 3x\geq 2
x< 0\: and\: x\geq \frac{2}{3}
x\: \epsilon \: \left ( -\infty,0 \right ]and\: x\: \epsilon \left [ \frac{2}{3},\infty \right ]
x\: \epsilon \: \left ( -\infty,0 \right ]\cup \left [ \frac{2}{3},\infty \right ]
Domain is  \left (-\infty,0\right ] \cup \left [ \frac{2}{3},\infty \right ]

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