Question

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

Answer 1

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

Explanation:

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]}