What is the domain and range of $f(x) = 1/(2x+4)$ ?

Question

3466 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-16T16:51:04

Domain: $(-oo, -2) uu (-2, + oo)$
Range: $(-oo, 0) uu (0, + oo)$

First, notice that you can rewrite your function as

$f(x) = 1/(2 * (x + 2))$

This function is defined for any value of $x in RR$ except the value that would make the denominator equal to zero.

More specifically, you need to exclude from the domain of the function the value of $x$ that would make

$x + 2 = 0 implies x = -2$

Therefore, the domain of the function will be $RR - {-2}$ , or $(-oo, -2) uu (-2, + oo)$ .

Notice that since you're dealing with a fraction that has a constant numerator, the function has no way of ever being equal to zero.

$f(x) !=0", "(AA)x in RR - {-2}$

The range of the function will thus be $RR - {0}$ , or $(-oo, 0) uu (0, + oo)$ .

graph{1/(2x + 4) [-6.243, 6.243, -3.12, 3.123]}

What is the domain and range of f(x) = 1/(2x+4)f(x) = 1/(2x+4)?