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###### Deepak Patra posted an Question
December 21, 2021 • 18:45 pm 30 points
• IIT JAM
• Mathematics (MA)

## (c) all real roots are positive 40. letf:r> r be a function with the property that for every y e r. the value of the expression sup xy -f(x)] is finite. define

(c) all real roots are positive 40. Letf:R> R be a function with the property that for every y e R. The value of the expression sup xy -f(x)] is finite. Define g(y) = sup [xy -f(x)] for y e R. Then (b) g is odd if f is even xeR XER (a) f must satisfy, lim =+ 00 x X f(X)+ fX) (d) f must satisfy lim -o b x x (c) g is even if f is even

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• ##### Deepak patra

what about option a and d ????

c is not right

• ##### Navdeep goyal 1

C check attachment

sir why you replace x to -x?????

g(y) for all x

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