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## Get ready for Algebra 2

### Course: Get ready for Algebra 2>Unit 4

Lesson 9: Intro to inverse functions

# Graphing the inverse of a linear function

Sal is given a line segment on the coordinate plane, and he graphs the inverse of the function represented by that segment.

## Want to join the conversation?

• Are all linear functions invertible around y=x?
• All functions are at least in part invertible (for some functions you have to only take a small part of the function in order for it to be invertible), but once you invert them, graphically they all look like they were mirrored about the line `y = x`.
• Sal said in his first video in inverse function that he will explain why he constrained the domain of function. Where is the video that explain the reason ?
• In Algebra 1, the first module is functions. Check it up, it's there
• Will the line Y=X stay the same or would something strange happen?
• how do you solve the inverse function of y=x^2 +2
• The inverse can be found by switching the x and y, then solving for y again.

So the inverse is x=y^2 +2
x-2=y^2
y=√(x-2)
• Can someone please explain to me the concept of the horizontal line test? I'm doing the domain and range with inverse functions exercise.
• The horizontal line test is used for figuring out whether or not the function is an inverse function. Picture a upwards parabola that has its vertex at (3,0). Then picture a horizontal line at (0,2). The line will touch the parabola at two points. This is how you it's not an inverse function.
• So i have never understood how to get Domain and Range of anything or where it comes from or why. I've tried again again to understand.... Maybe you could help me ?
• TRL, I think of domain as the possible values of x that will result in a point on a curve; and range are the possible values of y that could result in a point on a curve. Think of a parabola... any x can be substituted into the equation to get a y on the curve, so the domain is all real numbers. But our parabola has a minimum or maximum, so there's a point where the y-values stop being an option. That's a restriction on the range, that y can only be greater than or equal to the minimum, or less than or equal to the maximum, depending on the way it's facing. In this inverse video, the trick is to remember that the range of a function affects the domain of the inverse, and the domain of a function affects the range of the inverse :-)
• how to do the inverse of trigonometric functions?
• If the graphs of a function and its inverse function intersect, would the two graphs intersect on the line y=x? What is the possibility for the two graphs to intersect on other lines?