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MHT CET20225 Aug 2022Morning ShiftMathematicsInverse Trigonometric FunctionsActual

Considering only the Principal values of inverse function, the set x 0 / ⁻¹(2 x)+ ⁻¹ 3 x= 4

Options

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

Correct answer

A. is a singleton set.

Step-by-step solution

aligned & ⁻¹(2 x)+ ⁻¹(3 x)= 4 & ⁻¹ 2 x+3 x 1-2 x 3 x = ⁻¹(1) & 5 x 1-6 x^2 =1 & 5 x=1-6 x^2 & 6 x^2+5 x-1=0 & (x+1)(6 x-1)=0 aligned x=-1 or x= 1 6 But x 0 Hence x= 1 6 (only) i.e., single ton set

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