Menu Close

given-that-f-x-1-2-10-x-10-x-prove-that-2f-x-f-y-f-x-y-f-x-y-

Tinku Tara 0 Comments
Pin




Question Number 33688 by mondodotto@gmail.com last updated on 22/Apr/18
given that f(x)=(1/2)(10^x +10^(−x) ) prove that 2f(x) f(y)=f(x+y)+f(x−y)
giventhatf(x)=12(10x+10−x)provethat2f(x)f(y)=f(x+y)+f(x−y)
Answered by Rasheed.Sindhi last updated on 22/Apr/18
f(x)=(1/2)(10^x +10^(−x) ) f(y)=(1/2)(10^y +10^(−y) ) 2f(x) f(y)=2×(1/2)(10^x +10^(−x) )×(1/2)(10^y +10^(−y) ) =(1/2)(10^(x+y) +10^(−x−y) +10^(x−y) +10^(y−x) ) =(1/2)(10^(x+y) +10^(−(x+y)) +10^(x−y) +10^(−(x−y)) ) =(1/2) (10^(x+y) +10^(−(x+y)) )+(1/2)(10^(x−y) +10^(−(x−y)) ) =f(x+y)+f(x−y)
f(x)=12(10x+10−x)f(y)=12(10y+10−y)2f(x)f(y)=2×12(10x+10−x)×12(10y+10−y)=12(10x+y+10−x−y+10x−y+10y−x)=12(10x+y+10−(x+y)+10x−y+10−(x−y))=12(10x+y+10−(x+y))+12(10x−y+10−(x−y))=f(x+y)+f(x−y)

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *