What is the domain and range of $f (x) = \frac{x + 6}{2 x + 1}$ $f(x) = (x+6 )/ (2x+1)$ ?

Question

2854 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-16T10:13:57

The domain is $x in RR-{-1/2}$ .
The range is $y in RR-{1/2}$

As you cannot divide by $0$ , the denominator is $!=0$

Therefore,

$2x+1!=0$

$=>$ , $x"=-1/2$

The domain is $x in RR-{-1/2}$

In order to find the range, proceed as follows .

Let $y=(x+6)/(2x+1)$

$y(2x+1)=x+6$

$2xy+y=x+6$

$2xy-x=6-y$

$x(2y-1)=(6-y)$

$x=(6-y)/(2y-1)$

In order for $x$ to have solutions,

$2y-1!=0$

$y!=1/2$

The range is $y in RR-{1/2}$

graph{(x+6)/(2x+1) [-18.02, 18.01, -9.01, 9.01]}

What is the domain and range of f(x) = (x+6 )/ (2x+1) f(x)=x+62x+1f(x) = (x+6 )/ (2x+1) ?