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The domain of f(x) is (0,1) Then the dom...

The domain of `f(x)` is (0,1) 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
`f(x)` is defined for ` x in (0,1)`
So,`f(e^(x))+f("In"|x|)` is defined for
` 0 lt e^(x) lt 1 and 0 lt "In"|x| lt 1`
` or -oo lt x lt 0 and 1 lt |x| lt e`
`or x in (-oo,0 ) and x in (-e, -1) cup (1,e)`
` or x in (-e, -1)`
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