How do you find the domain and range of $f (x) = \frac{2}{x - 1}$ $f(x) = 2/(x-1)$ ?

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Answer 1 · 2015-09-02T21:11:40

The domain is $x \neq 1$ $color(red)(x≠1)$ ; the range is $y \neq 0$ $color(red)(y≠0)$ .

$f (x) = \frac{2}{x - 1}$ $f(x) = 2/(x-1)$

When $x = 1, y = \frac{2}{0}$ $x=1, y=2/0$ .

The value of $\frac{2}{0}$ $2/0$ is undefined, so $x$ $x$ cannot equal $1$ $1$ .

The domain is $x \neq 1$ $x≠1$ .

As $x$ $x$ becomes large and positive, the value of $y$ $y$ approaches zero but never reaches it.

The same thing happens as $x$ $x$ becomes large and negative.

$y$ $y$ can have any value except zero.

The range is is $y \neq 0$ $y≠0$ .

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How do you find the domain and range of f(x)=2x−1f(x) = 2/(x-1)?