Paragraph: Read the following write up carefully and answer the following questions: Consider a function f: R R such that (f(x)+f(z))(f(y)+f(t))=f(x y-z t)+f(x t+y z) where x, y, z, t R Question: If f: R R is the given function then in the

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Paragraph: Read the following write up carefully and answer the following questions: Consider a function f: R R such that (f(x)+f(z))(f(y)+f(t))=f(x y-z t)+f(x t+y z) where x, y, z, t R Question: If f: R R is the given function then in the interval (0, ) f(x) is

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Correct answer: A. non decreasing

If y=x in f(x) f(y)=f(x y) f (x^2 )=f^2(x) 0 Put x=t, y=z aligned & [f(x)+f(y)]^2=f (x^2+y^2 ) & f (x^2+y^2 )=f^2(x)+f^2(y)+2 f(x) f(y) f^2(x) & f (x^2+y^2 ) f (x^2 ) aligned f is non decreasing for positive x

Paragraph: Read the following write up carefully and answer the following questions: Consider a function f: R R such that (f(x)+f(z))(f(y)+f(t))=f(x y-z t)+f(x t+y z) where x, y, z, t R Question: If f: R R is the given function then in the interval (0, ) f(x) is

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