Let E 1 = 
and E 2 = 
.
(Here, the inverse trigonometric function sin –1 x assumes values in 
.)
Let f : E 1 → R be the function defined by f(x) = log e 
and g : E 2 → R be the function defined by g(x) = sin –1 
LIST-I LIST-II
(P) The range of f is (1) 
∪ 
(Q) The range of g contains (2) (0, 1)
(R) The domain of f contains (3) 
(S) The domain of g is (4) (– ∞ , 0) ∪ (0, ∞ )
(5) 
(6) (– ∞ , 0) ∪ 
The correct option is
Text Solution
Verified by ExpertsA
Sol. E 1 : 
> 0 ⇒ x ∈ (– ∞ , 0) ∪ (1, ∞ )
E 2 : –1 ≤ n 
⇒ 
⇒ 
⇒ (x – 1) ∈ 
∪ 
x ∈ 
Now 
∈ (0, ∞ ) – {1} ∀ x ∈ E 1 ⇒ n 
∈ (– ∞ , ∞ ) – {0}
sin –1 
∈ 
– {0}
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