Let D be the doma

The set of values ​​for which the function can be defined is domain of a real valued function.

We have,

In order to find domain of f(x) we need to find those real values of x which will give real value to f(x) after solving.

Now, f is a real valued function if 25-x² ≥ 0

⇒ 25-x² ≥ 0

⇒ -(x²-25) ≥ 0

On multiplying the inequality by -1 we get,

⇒ x²-25 ≤ 0

Note : The sign of inequality is reversed if it is multiplied by a negative quantity.

⇒ (x+5)(x-5) ≤ 0

⇒ x ∈ [-5,5]

Hence, Domain(f) = {x : x ∈ [-5,5] }