Question

Find the domain and range of the follwoing function.

h(x) = `sqrt(x + 5)/(5 + x)`

Answer 1

h(x) = `sqrt(x + 5)/(5 + x)` = `1/sqrt(x + 5), x ≠ -  5`

For x = –5, function h is not defined.

∴ x + 5 > 0 for function h to be well defined

∴ x > –5

∴ The domain of h = `(-5, ∞)`

Let y = `1/sqrt(x + 5)`

∴ y > 0

∴ The range of h = `(0, ∞)` or R⁺