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

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Answer 1 · 2018-06-10T13:14:23

Domain: $(- \infty, 0) \cup (0, + \infty)$ $(-oo,0)uu(0,+oo)$ Range: $(- \infty, + \infty)$ $(-oo,+oo)$

$g (x) = \frac{2}{x}$ $g(x) = 2/x$

$g (x)$ $g(x)$ is defined $\forall x \neq 0$ $forall x !=0$

Hence, the domain of $g (x)$ $g(x)$ is : $(- \infty, 0) \cup (0, + \infty)$ $(-oo,0)uu(0,+oo)$

Now consider the limit of $g (x)$ $g(x)$ as $x \to 0$ $x-> 0$ from below and from above.

$lim_(x->0^-) 2/x -> -oo$

$lim_(x->0^+) 2/x -> +oo$

Thus $g(x)$ has a vertical asymptote at $x=0$ .

The range of $g(x)$ is therefore $(-oo,+oo)$

We can visualise these results from the graph of $g(x)$ below.

graph{2/x [-10, 10, -5, 5]}

How do you find the domain and range of g(x)=2/xg(x)=2xg(x)=2/x?