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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

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

Grade:12

2 Answers

Ramesh V
70 Points
14 years ago

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

Askiitian.Expert Rajat
24 Points
14 years ago

Hi,

 

 

Since f(x) is a polynomial, Hence it is continuous, therefore lim x→2 f(x) = f(2) = 5

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