2.2 Functions: notation, domain, range, inverse

Domain and Range

Domain: All the allowable values for x

Range: All the possible values for y that result from the domain.

MIT grad shows a surefire way to find the domain of any function. To skip ahead: 1) For POLYNOMIAL only, skip to time 0:45. 2) For FRACTION only, skip to time 1:44. 3) For SQUARE ROOT only, skip to 5:08. 4) For SQUARE ROOT ON BOTTOM of Fraction, skip to 8:44. 5) For SQUARE ROOT ON TOP of Fraction, skip to 10:09. Nancy formerly of MathBFF explains the steps.

How to find inverse functions

https://youtu.be/-l7U3dEAGa4

There are three steps to finding the inverse function, if it exists. The first step is to replace the f(x) with just the variable y. Second, swap the x and y variables everywhere they appear in the equation. Third, solve for y again so that you have just "y=" on one side of the equation. If this relation is a function, you can then replace the y with the "f inverse x" notation, or f^-1(x). To know if it is a function, use the Vertical Line Test or consider the form of the equation. Remember that in a function equation, for every x you input into the equation, there can only be one corresponding y value. For an example problem, jump to 00:43 in the video.