vault backup: 2023-12-18 10:12:15

education/math/Inverse Functions.md

@@ -1 +1,8 @@
-For a function to have an inverse, it needs to have one $x$ for every $y$, and vice versa. You can use the horizontal line test to verify that the inverse of a function is valid. If you can draw a horizontal line and it crosses through two points at the same time at any height, the inverse is not a valid function.  
+For a function to have an inverse, it needs to have one $x$ for every $y$, and vice versa. You can use the horizontal line test to verify that the inverse of a function is valid. If you can draw a horizontal line and it crosses through two points at the same time at any height, the inverse is not a valid function. To get the inverse, you can switch the x and y of a function, and it will mirror the graph over the line $y = x$. 
+
+# Examles
+Given the below function:
+$$ y = \frac{1}{2}x + 3 $$
+You can find the inverse by switching the $x$ and $y$ values and solving for $y$:
+$$ x = \frac{1}{2}y + 3 $$
+The range of the inver