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

##### 1 Answer

Domain:

Range:

#### Explanation:

First, notice that you can rewrite your function as

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

This function is defined for any value of **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 + 2 = 0 implies x = -2#

Therefore, the domain of the function will be

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

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