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 –