The domain of the function f(x)=log10⁡5x−x241/2 is

We have f(x)=log10⁡5x−x241/2              (1)From (1), clearly, f(x) is defined for those values of x for which log10⁡5x−x24≥0or 5x−x24≥100or 5x−x24≥1or x2−5x+4≤0or (x−1)(x−4)≤0Hence, the domain of the function is [1, 4].