+ (x+4)0.5+4(x+4)0.5 ... (i) We have to find the domain of definition of f (x) Now, writing (I) in simplified form f (x) = x.
1+
2
√x+4
2−√x+4
+ √x+4+4√x+4 Using definition of square root function, clearly, f (x) is defined for x + 4 > 0 and 2 - √x+4 ≠ 0 ⇒ x > - 4 , x ≠ 0 So, domain of function f (x) = (- 4 , 0) ∪ (0 , ∞) Hence, option 'D' is correct