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NDA2025MathematicsInverse Trigonometric FunctionsActual

Consider the following for the two (02) items that follow: Let y = ⁻¹ (x - 4x^3 27 ) . What is y equal to?

Options

  1. A⁻¹ x
  2. B⁻¹ ( x 3 )
  3. C3 ⁻¹ x
  4. D3 ⁻¹ ( x 3 )

Correct answer

D. 3 ⁻¹ ( x 3 )

Step-by-step solution

Given y = ⁻¹ (x - 4x^3 27 ) Substitute x = 3 , which gives = x 3 or = ⁻¹ ( x 3 ) The expression becomes: y = ⁻¹ (3 - 4(3 )^3 27 ) y = ⁻¹ (3 - 4(27 ^3 ) 27 ) y = ⁻¹(3 - 4 ^3 ) Using the trigonometric identity (3 ) = 3 - 4 ^3 : y = ⁻¹( (3 )) y = 3 Substituting back the value of : y = 3 ⁻¹ ( x 3 ) Answer: 3 ⁻¹ ( x 3 )

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