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Let f(x)= 1+x^2 , then

Options

  1. Af(x y)=f(x) f(y)
  2. Bf(x y) f(x) f(y)
  3. Cf(x, y) f(x) f(y)
  4. Df(x y)=f(x)-f(y)

Correct answer

C. f(x, y) f(x) f(y)

Step-by-step solution

Given that, f(x)= 1+x^2 array ll & f(y)= 1+y^2 and & f(x y)= 1+x^2 y^2 array Now, | f(x y)=f(x) f(y) aligned 1+x^2 y^2 & = 1+x^2 1+y^2 & = (1+x^2 ) (1+y^2 ) aligned On squaring both sides, we get aligned & 1+x^2 y^2= (1+x^2 ) (1+y^2 ) & 1+x^2 y^2=1+y^2+x^2+x^2 y^2 aligned aligned & 1+x^2 y^2 1+x^2+y^2+x^2 y^2 & Hence, f(x y) f(x) f(y) aligned

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