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The domain of f(x)i s(0,1)dot Then the d...

The domain of `f(x)i s(0,1)dot` Then the domain of `(f(e^x)+f(1n|x|)` is `(a)(-1, e)` (b). `(1, e)` `(c).(-e ,-1)` (d) `(-e ,1)`

A

`(-1, e)`

B

`(1, e)`

C

`(e, 1)`

D

`(-e, 1)`

Text Solution

Verified by Experts

The correct Answer is:
C
Since f(x) is defined on (0,1) and
`g(x) = f(e^(x)) + f(log_(e)|x|)`. Therefore, g(x) exists, if
` 0 lt e^(x) lt and 0 log_(e)|x| lt 1`
`rArr -oo lt x lt 0 and 1 lt |x| lt e`
`rArr - oo, lt x lt 0 and 1 le |x| lt e`
`rArr x in (-oo, 0) and x in (-e,-1) uu (1,e)`
`rArr x in (-e,-1)`.
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