How to do this question, regarding f(x)?

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Answer 1 · 2018-03-05T09:49:08

Please refer to the Explanation.

#f : RR to RR : f(x)=sinx,; x in RR#.

To show that, #EE x,y in RR, s.t. f(x+y)nef(x)+f(y)#.

Take, #x=pi/6 and y=pi/3," so that, "x+y=pi/2.#

#:. f(x)=f(pi/6)=sin(pi/6)=1/2#,

#f(y)=f(pi/3)=sin(pi/3)=sqrt3/2#.

#:. f(x)+f(y)=(1+sqrt3)/2," whereas, "#

#f(x+y)=f(pi/2)=sin(pi/2)=1," showing that, "#

#f(x)+f(y)nef(x+y)#.