Domain and range

What is it?

Formulas

$$\operatorname{dom}\sqrt{x} = [0,\infty), \quad \operatorname{dom}\ln x = (0,\infty), \quad \sigma(\R) = (0,1)$$

Where it shows up in computing

• Floating point (IEEE 754)★★★★★frequentScientific computing and algorithms

  Outside the domain IEEE 754 returns NaN (sqrt(-1)) or ±∞ (log(0)) instead of failing.

Where it shows up in AI

• Activation functions★★★★★frequentAI and machine learning

  The range of the sigmoid, $(0,1)$, is why its output can be read as a probability.

Where is it used?

Computing topics reachable from here, through the chain of ideas that leads to them:

What depends on it

• Inverse functions