Find the domain and range of each of the following real valued function: `f(x)=(a x-b)/(c x-d)` .

Answer

dom `(f)=R-{(d)/(c)}," range "(f)=R-{(a)/(c)}`

Explanation

`f(x)=(ax-b)/(cx-d)` si not defined when `cx-d=0impliesx=(d)/(c)`
`:."dom "(f)=R-{(d)/(c)}`.
Let y=f(x). Then,
`y=(ax-b)/(cx-b)impliescxy-dy=ax-bimpliescxy=ax=dy-b`
`impliesx(cy-a)=dy-bimpliesx=(dy-b)/(cy-a)`.
Clearly, x is not defined when `cy-a=0impliesy=(a)/(c)`.
`:."dom "(f)=R-{(a)/(c)}`.