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Most Important Selected Qs for JEE AdvancedMathematicsInverse Trigonometric Functions

Consider f(x)= ⁻¹ ( 2 x 9-4 x^2 )- ⁻¹ ( x 3 ) . Identify which of the following statement(s) is(are) correct?

Options

  1. ANumber of solutions of the equation f(x)= (-x) is 2 .
  2. BNumber of solutions of the equation f(x)= (-x) is 1 .
  3. CIf f(x)-k=0 has a solution then number of integral values of k is 4 .
  4. DIf f(x)-k=0 has a solution then number of integral values of k is 3 .

Correct answer

C. If f(x)-k=0 has a solution then number of integral values of k is 4 .

Step-by-step solution

f(x)= ⁻¹ ( 2 x 9-4 x^2 )- ⁻¹ ( x 3 ) Domain of f(x) is x ( -3 2 , 3 2 )f(x)= ⁻¹ ( 2 x 3 )- ⁻¹ ( x 3 ) When, aligned & x ( -3 2 , 3 2 ) & ( - 2 , 2 )- ( 2 3 , 3 ) aligned Range of f(x) ( -7 6 + 6 ) Number of solution of f(x)= (-x) has only one solution f(x)-k=0 has number of integral solution k= -3,-2,-1,0 4 value

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