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