1.

If af(x) + bf(1/x) = x+1, x != 0, find f(x).

Answer»

Solution :Given AF(X) + BF(1/x) = x + 1 ...(i)
`because x != 0` replacing x by `(1)/(x)` in (i), we get
`af((1)/(x)) + bf (x) = (1)/(x) + 1` ....(ii)
Eliminating `f((1)/(x))` from (i) and (ii), we get
`(a^(2) - b^(2)) f(x) = a(x+1) - b((1)/(x) + 1) :. f(x) = (a(x+1)-b((1)/(x) + 1))/(a^(2)-b^(2))`


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