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COMEDK2023Evening ShiftMathematicsInverse Trigonometric FunctionsActual

Let f(x)= ⁻¹(3 x-1) , then domain of f(x) is equal to

Options

  1. A(0, 2 3 )
  2. B[- 2 3 , 2 3 ]
  3. C(- 2 3 , 2 3 )
  4. D[0, 2 3 ]

Correct answer

D. [0, 2 3 ]

Step-by-step solution

The function f(x) = ⁻¹(3x - 1) is defined when the argument of the inverse cosine function lies in the interval [-1, 1] . Therefore, we set the inequality: -1 3x - 1 1 Adding 1 to all parts of the inequality: -1 + 1 3x - 1 + 1 1 + 1 0 3x 2 Dividing by 3 throughout: 0 x 2 3 Thus, the domain of f(x) is [0, 2 3 ] . Answer: [0, 2 3 ]

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