If `a f(x+1)+b f(1/(x+1))=x,x !=-1,a != b,`then `f(2)` is equal to

Options

A. `f(2)=(2a+b)/(2(a^(2)-b^(2))`
B. `f(1)=0`
C. `f((1)/(2))=(a+2b)/(a^(2)-b^(2))`
D. `f(2)=(2a+b)/((a^(2)-b^(2)))`

Answer

A, B

Explanation

`af(x+1)+bf((1)/(x+1))=(x+1)-1` ..(i)
`af((1)/(x+1))+bf(x+1)=(1)/(x+1)=-1` . . .(ii)
`(1)xxa-(2)xxbimplies(a^(2)-b^(2))f(x+1)`
`=a(x+1)-a-(b)/(x+1)+b`
putting `x=1,f(2)=(2a+b)/(2(a^(2)-b^(2)))`