If for `xne0,af (x)+bf((1)/(x))=1/x-5,aneb,` then f (x).

Answer

N/a

Explanation

Given that
`af(x)+bf((1)/(x))=1/x-5" "...(1)`
Replace x by `1/x`
`af((1)/(x))+bf(x)=x-5" "...(2)`
Multiplying eq. (1) by a and eq. (2) by b
`a^(2)f(x)+abf((1)/(x))=a/x-5a`
`abf((1)/(x))+b^(2)f(x)=bx-5b`
On subtracting, we get
`(a^(2)-b^(2))f(x)=a/x-bx-5a+5b`
`impliesf(x)=(1)/(a^(2)-b^(2))((a)/(x)-bx-5a+5b).`