From 77565add5cd04557129dde7987c06ccf99382253 Mon Sep 17 00:00:00 2001 From: zleyyij Date: Mon, 18 Dec 2023 10:17:15 -0700 Subject: [PATCH] vault backup: 2023-12-18 10:17:15 --- education/math/Inverse Functions.md | 9 +++++++-- 1 file changed, 7 insertions(+), 2 deletions(-) diff --git a/education/math/Inverse Functions.md b/education/math/Inverse Functions.md index 13dc21a..acfc17e 100644 --- a/education/math/Inverse Functions.md +++ b/education/math/Inverse Functions.md @@ -1,8 +1,13 @@ 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 +# Examples 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 \ No newline at end of file +The range of the inverse is the same as the domain of the original. +You can verify by taking $f \circ g$, and simplifying. + + +Given the below function: +$$ f(x) = \frac{x+ \ No newline at end of file