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If f(x) is a polynomial satisfying 2+f(x) f(y) = f(x) + f(y) + f(xy) for all real x and y and f(2) = 5. Then lim x→2 f(x) is
(a)5 (b)25 (c)4 (d)nonne of these
for y=2,we have : 2+5f(x) = f(x)+5+f(2x)
4f(x)=3+f(2x)
putting x=0 gives f(0)=1
x=1 gives f(0)=2
x=2 gives f(4)=17
which clearly indicates f(x)=x2 + 1
limit x->2 f(x) is 5
option A
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regards
Ramesh
Hi,
Since f(x) is a polynomial, Hence it is continuous, therefore lim x→2 f(x) = f(2) = 5
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