Answer :

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] }

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