Question

Find the domain and range of x

Answer 1

`\textsf {Domain} : -\infty \: < x < \infty \\\textsf {In interval notation: } (-\infty, \infty)}`

`\textsf {Range: } f\left(x\right)\le \:2 \\\textsf {In interval notation:} \:(-\infty \:,\:2]`

Explanation:

There are no undefined points for the function. So the domain is the set of all x values

The domain of x is (-∞, ∞) so x can be negative or positive. However, |x| is always positive

So if the inequality |x| + y ≥ 2 is to hold good then y has to be less than equal to 2, otherwise the left side drops below 2 and the inequality is not satisfied.

So the range is the set of all values in the interval (-∞, 2)

Check out the graph for a visual interpretation