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KVPY2013MathematicsFunctions

Let f(x)= 2-x-x² and g(x)= x . Which of the following statements are true? (I) Domain of f ((g(x))² )= Domain of f(g(x)) (II) Domain of f(g(x))+g(f(x))= Domain of g(f(x)) (III) Domain of f(g(x))= Domain of f(g(x)) (V) Domain of g ((f(x))³ )= Domain of f(g(x)) (IV) Domain of g ((f( x ))³ )= Domain of f( ~g ( x ))

Options

  1. AOnly (I)
  2. BOnly (I) and (II)
  3. COnly (III) and (IV)
  4. DOnly (I) and (IV)

Correct answer

B. Only (I) and (II)

Step-by-step solution

Domain of f(g(x)) is R array l 2- x- ² x 0 ( x+2)( x-1) 0 -2 x 1 x R array Domain of g(f(x)) is [-2,1] array c ( 2-x-x² ) 2-x-x² 0 array Domain of f (g(x)² ) is R array l 2- ² x- ⁴ x 0 ( ² x+2 ) ( ² x-1 ) 0 -1 x 1 x R array Domain of g ( f ^ ( x ) . is Domain of g ( f ( x ) i.e., [-2,1]

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