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Question
Find the domain and range of the follwoing function.
h(x) = `sqrt(x + 5)/(5 + x)`
Solution
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+
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