Question

Find the domain and range of the function f(x) = `1/sqrt(x - 5)`

Answer 1

Given that: f(x) = `1/sqrt(x - 5)`

Here, it is clear that f(x) is real when x – 5 > 0

⇒ x > 5

Hence, the domain = `(5, oo)`

Now to find the range put

f(x) = y = `1/sqrt(x - 5)`

⇒ `sqrt(x - 5) = 1/y`

⇒ `x - 5 = 1/y^2`

⇒ x = `1/y^2 + 5`

For x ∈ `(5, oo)`, y ∈ R⁺

Hence, the range of f = R⁺.