From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Wed, 6 Feb 2019 01:32:19 +0000 (+1100)
Subject: fractional power functions
X-Git-Tag: yr12~259
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/334dfa5a0247da793421d47ed583933104b3720a

fractional power functions
---

diff --git a/methods/transformations.md b/methods/transformations.md
index ae201e0..503257f 100644
--- a/methods/transformations.md
+++ b/methods/transformations.md
@@ -46,4 +46,14 @@ $b$ - translation from $x$-axis ($y$-shift)
 $f(-x)=-f(x)$
 
 #### $n$ is even and $n>1$:
-$f(-x)=f(x)$
\ No newline at end of file
+$f(-x)=f(x)$
+
+### Function $f(x)=x^{-1 \over n}$ where $n \in \mathbb{Z}^+$
+
+Mostly only on CAS.
+
+We can write $x^{-1 \over n} = {1 \over {x^{1 \over n}}} = {1 \over ^n \sqrt{x}}$n. Domain is:  $\begin{cases} \mathbb{R} \setminus \{0\}\hspace{0.5em} \text{ if }n\text{ is odd} \\ \mathbb{R}^+ \hspace{2.6em}\text{if }n\text{ is even}\end{cases}$
+
+**Odd and even functions:**  
+Function is even if it can be reflected across $y$-axis $\implies f(x)=f(-x)$  
+If $n$ is odd, then $f$ is an odd function since $f(-x)=-f(x) \implies f(x)=-f(x)$
\ No newline at end of file