UPSEE Solved Model Paper 7

Given :
f (x) =

3

4−x2

+log10(x3−x) ... (i)
We have to find the domain of f (x)
Let f1 =

3

4−x2

, then f1 will be defined when
4 - x2 ≠ 0
⇒ x2 ≠ 4
⇒ x ≠ ± 2 ... (ii)
Let f2 = log10(x3−x)
Using definition of logarithmic function, we get
⇒ x(x2−1) > 0
⇒ x (x - 1) (x + 1) > 0
From wavy curve method, we have

x ∊ (- 1 , 0) ∪ (1 , ∞) ... (ii)
x ∊ ( - 1 , 0) ∪ (1 , ∞) ... (ii)
From (ii) & {iii}, we get
domain = (- 1 , 0) ∪ (1 , 2) ∪ (2 , ∞)
Hence, option 'D' is correct.