How do you find the domain and range of $f (x) = \frac{5}{x - 3}$ $f(x)=5/(x-3)$ ?

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How do you find the domain and range of $f (x) = \frac{5}{x - 3}$ $f(x)=5/(x-3)$ ?

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Answer 1 · 2018-05-20T17:13:16

The domain is $x \in (- \infty, 3) \cup (3, + \infty)$ $x in (-oo,3)uu(3,+oo)$ . The range is $y \in (- \infty, 0) \cup (0, + \infty)$ $y in (-oo,0)uu(0,+oo)$

Explanation:

The denominator must be $\neq 0$ $!=0$

Therefore,

$x - 3 \neq$ $x-3!=$

$\Rightarrow$ $=>$ , $x \neq 3$ $x!=3$

The domain is $x \in (- \infty, 3) \cup (3, + \infty)$ $x in (-oo,3)uu(3,+oo)$

To find the range, proceed as follows :

Let $y = \frac{5}{x - 3}$ $y=5/(x-3)$

$y (x - 3) = 5$ $y(x-3)=5$

$y x - 3 y = 5$ $yx-3y=5$

$y x = 5 + 3 y$ $yx=5+3y$

$x = \frac{5 + 3 y}{y}$ $x=(5+3y)/(y)$

The denominator is $\neq 0$ $!=0$

$y \neq 0$ $y!=0$

The range is $y \in (- \infty, 0) \cup (0, + \infty)$ $y in (-oo,0)uu(0,+oo)$

graph{5/(x-3) [-18.02, 18.02, -9.01, 9.02]}

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How do you find the domain and range of $f (x) = \frac{5}{x - 3}$ $f(x)=5/(x-3)$ ?

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Explanation:

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How do you find the domain and range of $f (x) = \frac{5}{x - 3}$ $f(x)=5/(x-3)$ ?