Let f(x) =√{2-x-x^2} and g(x)=\cos 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 g (f(x ))(IV) Domain of g((f(x ) )^3 ) = Domain of f(g (x ))

Question

Let f(x) =√{2-x-x^2} and g(x)=\cos 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 g (f(x ))(IV) Domain of  g((f(x ) )^3 ) = Domain of f(g (x ))

Examsnet · Accepted Answer

Correct Answer is :  Only (I) and (II)

KVPY SX SB Exam 2013 Question Paper