Question

If for non zero x, af(x) + bf(1/x) = 1/x - 5, where a ≠ b, find f(x).

Answer 1

We have

af(x) + bf(1/x) = 1/x - 5 ....(i)

Replace xby 1/x, we get

af(1/x) + bf(x) = x - 5    .....(ii)

Multiplying (i) by a (ii) by b and subtracting, we get

(a² - b²)f(x) = a(1/x - 5) - b(x - 5)

f(x) = (a(1/x - 5) - b(x - 5))/(a² - b²)