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

Explanation

Since, f(x) is defined for all real values of x, except for the case when bx – a = 0 or `x = a/b`. Domain (f) =` R – (a/b)`

Suppose 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) `

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