What is the domain and range of $g(x)=2/(x+5)$ ?

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Answer 1 · 2017-02-25T14:29:30

The domain of $g(x)$ is $D_g(x)=RR-{-5}$
The range of $g(x)$ is $R_g(x)=RR-{0}$

As you cannot divide by $0$ , $x!=-5$

The domain of $g(x)$ is $D_g(x)=RR-{-5}$

To find the range, we need $g^-1(x)$

Let $y=2/(x+5)$

$(x+5)y=2$

$xy+5y=2$

$xy=2-5y$

$x=(2-5y)/y$

Therefore,

$g^-1(x)=(2-5x)/x$

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

This is the range of $g(x)$

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

What is the domain and range of g(x)=2/(x+5)g(x)=2/(x+5)?