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

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Answer 1 · 2018-05-01T09:20:37

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

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

The denominator is $!=0$

Therefore,

$x+3!=0$

$x!=-3$

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

Also,

$y(x+3)=7$

$yx+3y=7$

$yx=4-3y$

$x=(4-3y)/(y)$

The denominator is $!=0$

Therefore

$y!=0$

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

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

How do you find the domain and range of f(x) = 7/(x+3)f(x) = 7/(x+3)?