Question

Find the domain and range of square root of x-5

Answer 1

Domain : { x ∈ R ∣ x ≥ −5}

Range : {f (x) ∈ R ∣ f(x) ≥ 0 }

Explanation

We have:

$f(x) = \sqrt{x + 5}$

The domain of any square root function is dependent on its argument.

The argument must be greater than or equal to zero:

$x + 5 \geqslant 0 \\ x \geqslant - 5$

The square root function never produces a negative result.

So the range will be greater than or equal to zero as well:

$f(x) \geqslant 0$

Therefore for the function

$f(x) = \sqrt{x + 5}$

the domain is { x ∈ R ∣ x ≥ −5}

the range is {f (x) ∈ R ∣ f(x) ≥ 0 }

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