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

Explanation

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

Suppose `f (x) = (ax - b)/(cx - d) = y`

`ax – b = y(cx – d) `

`ax – b = cxy – dy `

`ax – cxy = b – dy `

`x(a – cy) = b – dy `

`∴ x = (b - dy)/(a - cy) `

When `a – cy = 0 or y = a/c, `
Thus, f(x) cannot take the value` a/c`. ∴ Range (f) `= R – (a/c)
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