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If f(x)=(a-x)/(a+x), the domain of f^(-1...

If `f(x)=(a-x)/(a+x)`, the domain of `f^(-1)(x)` contains

A

`(-oo,oo)`

B

`(-oo,-1)`

C

`(-1,oo)`

D

`(0,oo)`

Text Solution

Verified by Experts

The correct Answer is:
B, C, D
Let `y=f(x)=(a-x)/(a+x)impliesay+xy=a-x`
`therefore x=(a(1-y))/((1+y))=f^(-1)(y)impliesf^(-1)(x)=(a(1-x))/((1+x))`
`therefore f^(-1)(x)` is not defined for x = - 1.
Domain of `f^(-1)(x)` belongs to `(-oo,-1)uu(-1,oo)`.
Now, for a = - 1, given function f(x) = - 1, which is constant.
Then, `f^(-1)(x)` is not defined.
`therefore ane-1`
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