Let D be the domain of the real valued function f defined by 
. Then, write D.
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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