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

Question

asked Aug 9, 2019 106k views

1 Answer

Jason Shirk · Answer 1 · 2019-08-15T09:10:59+0000

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
and
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