Let E_1=\{X∊\mathbb{R}:x\neq1andx/{x-1} > 0\} and E_2=\{X∊R_1:\sin^{-1}(\text{\log}_e(x/{x-1}))\text{is a real number}\}.(Here the inverse trigonometric function function \sin^{-1} assume values in [-\pi/2,\pi/2]) Let f:E_1\to\mathbb{R} be the function defined by f(x)=\text{\log}_e(x/{x-1}) and g:E_2\to\mathbb{R} be the function defined by g(x)=\sin^{-1}(\text{\log}(x/{x-1})) List - I List - II P. The range of f is 1. (-\infty,1/{1-e}]\cup[e/{e-1},\infty) Q. The range of g contains 2. (0, 1) R. The domain of f contains 3. [-1/2,1/2] S. The domain of g is 4. (-\infty,0]\cup(0,\infty) 5. (-\infty,e/{e-1}] 6. (-\infty,0)\cup(1/2,e/{e-1}] The correct options is: P Q R S A) 4 2 1 1 b) 3 3 6 5 c) 4 2 1 6 D) 4 3 6 5 [JEE Adv 2018 P2]

Functions

Section: Mathematics

Question : 16 of 30

Marks: +1, -0

Let E1={X∊ℝ:x≠1and

x−1

>0} and E2={X∊R1:sin−1(loge(

x−1

))is a real number}

.(Here the inverse trigonometric function function sin−1 assume values in [−

])
Let f:E1→ℝ be the function defined by f(x)=loge(

x−1

) and g:E2→ℝ be the function defined by g(x)=sin−1(log(

x−1

))

List - I

List - II

P. The range of f is

1. (−∞,

1−e

]∪[

e−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. (−∞,

e−1

]

6. (−∞,0)∪(

e−1

]

The correct options is:

[JEE Adv 2018 P2]

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