Question

Find the domain and range of the following function.

g(x) = `(x + 4)/(x - 2)`

Answer 1

g(x) = `(x + 4)/(x - 2)`

g(x) is not defined only for x = 2

∴ Domain = {x/x ∈ R, x ≠ 2} = R – {2}

Let y = `(x + 4)/(x - 2)`

∴ xy – 2y = x + 4

∴ xy – x = 2y + 4

∴ x(y – 1) = 2y + 4

∴ x = `(2y + 4)/(y - 1)`

If y = 1, we cannot find x such that g(x) = 1

∴ Range = {y/y ∈ R, y ≠ 1} = R – {1}

∴ Domain = {x/x ∈ R, x ≠ 2} = R – {2}

Range = {y/y ∈ R, y ≠ 1} = R – {1}