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Given that f(x) = 1-x x . What is the domain of f-1(x)? A) R B) R, x ≠ 0 C) R, x ≠ 1 D) R, x ≠ -1

User Fariz Azmi
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1 Answer

1 vote

Answer:

The required domain is
x\\e -1


Explanation:

The given function is


f(x)=(1-x)/(x)


We need the inverse of this function.


We first of all have to let
y=f(x).

This implies that,


y=(1-x)/(x)


Next, we interchange
x and
y to obtain,


x=(1-y)/(y)


We make y the subject to get,



xy=1-y



xy+y=1



(x+1)y=1



y=(1)/(1+x)


The inverse function is


f^(-1)(x)=(1)/(1+x)


The domain of this function is


x+1\\e 0



\Rightarrow x\\e -1


The correct answer is D






User Jason Shirk
by
7.9k points

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