What is the range of the function $f(x) = 1 / (x-2)$ ?

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Answer 1 · 2017-05-14T08:45:03

The range of $f(x)$ is $=RR-{0}$

The range of a function $f(x)$ is the domain of the function $f^-1(x)$

Here,

$f(x)=1/(x-2)$

Let $y=1/(x-2)$

Interchanging $x$ and $y$

$x=1/(y-2)$

Solving for $y$

$y-2=1/x$

$y=1/x-2=(1-2x)/x$

Therefore,

$f^-1(x)=(1-2x)/(x)$

The domain of $f^-1(x)$ is $=RR-{0}$

Therefore,

The range of $f(x)$ is $=RR-{0}$
graph{1/(x-2) [-12.66, 12.65, -6.33, 6.33]}

What is the range of the function f(x) = 1 / (x-2)f(x) = 1 / (x-2)?