Answers:

(i)

f(x) is defined for all real values of x, except when bx – a = 0 or x = a/b.

Domain (f) = R – (a/b)

Consider,

f (x) = y

(ax+b)/(bx-a) = y

ax + b = y(bx – a)

ax + b = bxy – ay

ax – bxy = –ay – b

x(a – by) = –(ay + b)

∴ x = – (ay+b)/(a-by)

If, a – by = 0 or y = a/b

f(x) cannot take the value a/b.

∴ Range (f) = R – (a/b)

(ii)

f(x) is defined for all real values of x, except when cx – d = 0 or x = d/c. Domain (f) = R – (d/c)

Consider, f(x) = y

(ax-b)/(cx-d) = y

ax – b = y(cx – d)

ax – b = cxy – dy

ax – cxy = b – dy

x(a – cy) = b – dy

∴ x = (b-dy)/(a-cy)

a – cy = 0 or y = a/c,

f(x) cannot take the value a/c.

∴ Range (f) = R – (a/c)