What is the domain and range of $f(x) = 1/(x + 3)$ ?

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Answer 1 · 2017-03-14T13:06:36

The domain of is $=RR-{-3}$
The range is $=RR-{0}$

As you cannot divide by $0$ , $x!=-3$

The domain of $f(x)$ is $D_f(x)=RR-{-3}$

To find the range, we need the domain of $f^-1(x)$

Let, $y=1/(x+3)$

$x+3=1/y$

$x=1/y-3=(1-3y)/y$

Therefore,

$f^-1(x)=(1-3x)/x$

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

So, the range is $=RR-{0}$

What is the domain and range of f(x) = 1/(x + 3)f(x) = 1/(x + 3)?