From: Andrew Lorimer 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