How do you find the domain and range of $f (x) = \frac{7}{x + 3}$ $f(x) = 7/(x+3)$ ?

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How do you find the domain and range of $f (x) = \frac{7}{x + 3}$ $f(x) = 7/(x+3)$ ?

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Answer 1 · 2018-05-01T09:20:37

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:

Let $y = \frac{7}{x + 3}$ $y=(7)/(x+3)$

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

Therefore,

$x + 3 \neq 0$ $x+3!=0$

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

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

Also,

$y (x + 3) = 7$ $y(x+3)=7$

$y x + 3 y = 7$ $yx+3y=7$

$y x = 4 - 3 y$ $yx=4-3y$

$x = \frac{4 - 3 y}{y}$ $x=(4-3y)/(y)$

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

Therefore

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

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

graph{(y-((7)/(x+3)))(y-0)=0 [-36.53, 36.52, -18.28, 18.27]}

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How do you find the domain and range of $f (x) = \frac{7}{x + 3}$ $f(x) = 7/(x+3)$ ?

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Explanation:

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How do you find the domain and range of $f (x) = \frac{7}{x + 3}$ $f(x) = 7/(x+3)$ ?