Question

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

Answer 1

Answer:

The required domain is $x\ne -1$

Step-by-step explanation:

The given function is

$f(x)=\frac{1-x}{x}$

We need the inverse of this function.

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

This implies that,

$y=\frac{1-x}{x}$

Next, we interchange $x$ and $y$ to obtain,

$x=\frac{1-y}{y}$

We make y the subject to get,

$xy=1-y$

$xy+y=1$

$(x+1)y=1$

$y=\frac{1}{1+x}$

The inverse function is

$f^{-1}(x)=\frac{1}{1+x}$

The domain of this function is

$x+1\ne 0$

$\Rightarrow x\ne -1$

The correct answer is D