FunctionHard
Question
If f(x) is defined on (0, 1) then the domain of definition of f(ex) + f(ln | x | ) is -
Options
A.(-e, -1)
B.(-e, -1) υ (1, e)
C.(-∞, -1) υ (1, ∞)
D.(-e, e)
Solution
f(ex) + f(ln | x | ) x ∈ (0, 1)
Now 0 < ex < 1 & 0 < ln | x | < 1
⇒ - ∞ < x < 0 ......(i)
⇒ 1 < | x | < e
⇒ (-e, -1) υ (1, e) ...(ii)
from (i) and (ii)
domain of x is (-e, -1)
Now 0 < ex < 1 & 0 < ln | x | < 1
⇒ - ∞ < x < 0 ......(i)
⇒ 1 < | x | < e
⇒ (-e, -1) υ (1, e) ...(ii)
from (i) and (ii)
domain of x is (-e, -1)
Create a free account to view solution
View Solution FreeMore Function Questions
Let function f : R → R be defined by f(x) = 2x + sin x for x ∈ R Then, f is...Let g (x) = 1 + x - [ x ] and f (x) =. Then for all x, f (g (x)) is equal to (where [.] denotes greatest integer functio...Let f(x) = x2 and g(x) = sinx for all xε R. Then the set of all x satisfying (f o g o g o f ) (x) = (g o g o f ) (x...Let f : R → R be a function defined by f(x) = x3 + x2 + 3x + sin x. Then f is:...f(x) = cos √x, correct statement is -...