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