The domain of the function given by f(x) = 1/√{x+[x]} is given by

Question

The domain of the function given by \(f(x) =\frac{1}{\sqrt{x+[x]}}\) is given by

(a) (0, ∞) 

(b) (– ∞, ∞) 

(c) (– ∞, 0) 

(d) [0, ∞)

Answer 1

Answer : (a) (0, ∞) 

f(x) = \(\frac{1}{\sqrt{x+[x]}}\) 

We know that,

Also, f (x) = \(\frac{1}{\sqrt{x+[x]}}\) is defined for all x satisfying x + [x] > 0 

∴  Domain of f (x) = (0, ∞).