FunctionMedium
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)
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