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If ƒ is a function such that ƒ(0)=2,ƒ(1)=3 and ƒ(x+2)=2ƒ(x)-ƒ(x+1) for every real x then ƒ(5) is...........

If ƒ is a function such that ƒ(0)=2,ƒ(1)=3 and                       ƒ(x+2)=2ƒ(x)-ƒ(x+1) for every real x then ƒ(5) is...........

Grade:12

1 Answers

Pratham Ashish
17 Points
12 years ago

hi,

 in,   ƒ(x+2)=2ƒ(x)-ƒ(x+1) ...................(1)

put x= 0. we get

   ƒ(2)=2ƒ(0)-ƒ(1)

         =  2 *2  - 3 = 1  

put x =1 ,

   ƒ(3)=2ƒ(1)-ƒ(2)

         =  2* 3 - 1 = 5

put ,  x = 2,

    ƒ(4)=2ƒ(2)-ƒ(3)

           =  2* 1 - 5 = -3 

put, x= 3 

    ƒ(5)=2ƒ(3)-ƒ(4)

          =  2*5 - (-3) = 13 

   ans...ƒ(5)  = 13

   

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