How do you find the domain and range for $f (x) = \frac{x + 2}{x + 7}$ $f(x)= (x+2)/(x+7)$ ?

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Answer 1 · 2017-11-04T06:52:34

The domain is $x in RR-{-7}$ . The range is $y in RR-{1}$

The function is $f(x)=(x+2)/(x+7)$

The denominator must be $!=0$

Therefore,

$x+7!=0$ , $=>$ , $x!=-7$

The domain is $x in RR-{-7}$

Let $y=(x+2)/(x+7)$

$y(x+7)=x+2$

$xy+7y=x+2$

$xy-x=2-7y$

$x(y-1)=2-7y$

$x=(2-7y)/(y-1)$

The denominator is $!=0$

$y-1!=0$ , $=>$ , $y!=1$

The range is $y in RR-{1}$

graph{(x+3)/(x+7) [-32.99, 24.74, -14.6, 14.27]}

How do you find the domain and range for f(x)= (x+2)/(x+7)f(x)=x+2x+7f(x)= (x+2)/(x+7)?