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Cosider f(x)=1-e^((1)/(x)-1) Q. If S i...

Cosider `f(x)=1-e^((1)/(x)-1)`
Q. If S is the range of f(x), then S is

A

`(-infty,infty)`

B

`(-infty,1)`

C

`(-infty,1)`

D

`(-infty,1)-{(1-(1)/(e))}`

Text Solution

Verified by Experts

The correct Answer is:
B
`e^((1)/(x)-1)=1-yge0`
i.e., `(1)/(x)-1=l n(1-y)`
i.e., `(1)/(x)=1+l n(1-y)=l n (1-y)`
`becausex(1)/(l ne(1-y))`
`because(e(1-y)ne1`
i.e., `yne1-(1)/(e)`
`becauseS=(-infty,1)-{1-(1)/(e)}`
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