Write the domain and the range of the function,
Question:

Write the domain and the range of the function, $f(x)=\frac{a x+b}{b x-a}$

Solution:

(i) domain

$f(x)=\frac{a x+b}{b x-a}$

As f(x) is a polynomial function whose domain is R except for the points where the denominator becomes 0.

Hence $x \neq b$

Domain is $\mathrm{R}-\{\underline{b}\}$

(ii) Range

Let $\mathrm{y}=\frac{a x+b}{b x-a}$

$Y(b x-a)=a x+b$

byx $-a y=a x+b$

byx $-a x=a y+b$

$x(b y-a)=a y+b$

x =$\frac{a y+b}{b y-a}$

x is not defined when denominator is zero.

by $-a \neq 0$

y≠a/b

Range is R-{a/b}.