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Paragraph: f(x) satisfies the relation f(x)- ₀^ / 2 x t f(t) d t= x Question: If f(x)=2 has at least one real root, then

Options

  1. A[1,4]
  2. B[-1,2]
  3. C[0,1]
  4. D[1,3]

Correct answer

D. [1,3]

Step-by-step solution

aligned & f(x)- x ₀^ / 2 cost f(t) d t= x & f(x)-P x= x & or f(x)=(P+1) x & Where P= ₀^ / 2 t f(t) d t & = ₀^ / 2 cost (P+1) t d t & = (P+1) 2 ₀^ / 2 2 t d t & P= (P+1) 2 P= 2- & f(x)= ( 2- +1 ) x=2 & x=2- & [1,3] & ₀^ / 2 2 2- x d x=3 & = 4 3 aligned

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