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KCET2015MathematicsDifferential Equations

[ f(x)= 1 2 - ( x 2 )-1 Find domain of ( (f+g) )

Options

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

Correct answer

B. ( (- 1 2 , 1 ] )

Step-by-step solution

Given that, f(x)= 1 2 - ⁻¹ ( x 2 ) and g(x)= 3+4 x-4 x² Since, f x() is defined in (-1,1) So, g(x) to defined, we have 3+4 x-4 x² 04 x²-4 x-3 0 4 x²-4 x+1-4 0 (2 x-1)²-4 0 (2 x-1)² 4 -2 2 x-1 2 -1 2 x 3 - 1 2 x 3 2 Therefore, domain of (f+g)= (- 1 2 , 1 )

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