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MHT CET202310 May 2023Morning ShiftMathematicsInverse Trigonometric FunctionsActual

Considering only the principal values of an inverse function, the set A = x 0 / ⁻¹ x+ ⁻¹ 6 x= 4

Options

  1. Ais an empty set.
  2. Bis a singleton set.
  3. Ccontains more than two elements.
  4. Dcontains two elements.

Correct answer

B. is a singleton set.

Step-by-step solution

Consider, ⁻¹ x+ ⁻¹ 6 x= 4 aligned & ⁻¹ ( 7 x 1-6 x^2 )= 4 & [ ⁻¹(x)+ ⁻¹(y)= ⁻¹ ( x+y 1-x y ) ] & 7 x 1-6 x^2 =1 & 7 x=1-6 x^2 & 6 x^2+7 x-1=0 & x= -7 73 12 & Since x 0 & x= -7+ 73 12 aligned A is a singleton set.

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