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If `f(x+y)=f(x)+f(y)-x y-1AAx , y in Ra n df(1)=1,`then the number of solution of `f(n)=n , n in N ,`is0 (b)1 (c) 2(d) more than 2 |
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Answer» Correct Answer - B Given `f(x+y)=f(x)+f(y)=xy=1 AA x, y in R` `f(1)=1,f(2)=f(1+1)=f(1)+f(1)-1-1=0` `f(3)=f(2+1)=f(2)+f(1)-2xx1 -1= -2` `f(n+1) = f(n)+f(1)-n-1=f(n)-n lt f(n)` Thus, `f(1) gt f(2) gt f(3) gt …, and f(1) =1.` Therefore, `f(1)=1 and f(n) gt 1, " for " n gt 1.` Hence, ` f(n)=n, n in N,` has only one solution `n=1.` |
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