Find the domain and range of each of the following real valued functions:

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

When, f(x) will be undefined as the division result will be indeterminate.

Thus, domain of f = R –

Let f(x) = y

⇒ ax + b = y(bx – a)

⇒ ax + b = bxy – ay

⇒ ax – bxy = –ay – b

⇒ x(a – by) = –(ay + b)

Clearly, when a – by = 0 or, x will be undefined as the division result will be indeterminate.

Hence, f(x) cannot take the value.

Thus, range of f = R –