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f(x) is a polynomial such that f(x)f(y)=f(x)+f(y)+f(xy)-2 for all real x nd y. also, f(2)=5. find f(3)

f(x) is a polynomial such that f(x)f(y)=f(x)+f(y)+f(xy)-2 for all real x nd y. also, f(2)=5. find f(3)

Grade:11

1 Answers

Sanjeev Malik IIT BHU
101 Points
10 years ago

f(2)= 22+1

first put x=2, y=2

f(2).f(2)= f(2)+f(2)+f(4)-2

5*5= 5+5+f(4) -2

f(4)=17 = 42+1

now put x=1,y=4

solving we get f(1)=2 = 12+1

now put x=2,y=4

solving f(8)=65= 82+1

see the pattern f(3)= 32+1 = 10

f(3)=10

 

 

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