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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