UPSEE Solved Model Paper 7

Given:
f (x) = x.

1+2(x+4)−0.5

2−(x+4)0.5

+ (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