Za
![](https://static.elitesecurity.org/tex/0198861716c4c197ff74e0edf16f5cf1.png)
je
![](https://static.elitesecurity.org/tex/2fa95a4714b27bcf3fd7717fa744d1f0.png)
.
Indukcijom se dokazuje da je,
![](https://static.elitesecurity.org/tex/86da8270595b27dd92da9d7ce5e04ccb.png)
.
Otuda je
![](https://static.elitesecurity.org/tex/7ff32d8dcc85f93a0f4d3890157ee482.png)
.
Jedini racionalni brojevi koji su
![](https://static.elitesecurity.org/tex/bd2b320696c94ea17dd122cd137b965c.png)
-ti stepen racionalnog broja za svako
![](https://static.elitesecurity.org/tex/bd2b320696c94ea17dd122cd137b965c.png)
su 0 i 1.
![](https://static.elitesecurity.org/tex/2ce0867f28d18b3b82ffe54cb9c67879.png)
,
![](https://static.elitesecurity.org/tex/17d3e4fa3c7c19a7202317f544a32aae.png)
,
![](https://static.elitesecurity.org/tex/f912da7ffa13f654c56082254540e791.png)
,
ili
![](https://static.elitesecurity.org/tex/2f795191bef9f94f67ddc3dab83af94f.png)
,
![](https://static.elitesecurity.org/tex/ddd220ead7e3314f8429d4238b0c6236.png)
,
![](https://static.elitesecurity.org/tex/8c25816a5665e1d1a08500bd09e42fd3.png)
.
U svakom od slučajeva treba ispitati funkciju u nuli i na negativnim racionalnim brojevima.
Ako je
![](https://static.elitesecurity.org/tex/2ce0867f28d18b3b82ffe54cb9c67879.png)
, onda je
![](https://static.elitesecurity.org/tex/592152ff193cb3c0d425bbfd25758051.png)
,
![](https://static.elitesecurity.org/tex/0e4e60960c876b241b06d297efa21174.png)
,
![](https://static.elitesecurity.org/tex/3bde06c38bad1ec3b90b49c1358106c9.png)
,
![](https://static.elitesecurity.org/tex/a18b01df1c6ea32270c636076d4b640d.png)
.
Ako je
![](https://static.elitesecurity.org/tex/2f795191bef9f94f67ddc3dab83af94f.png)
, onda je
![](https://static.elitesecurity.org/tex/70b3d1858c699fbd46bcafa3015a8867.png)
,
![](https://static.elitesecurity.org/tex/45a93894bfefb39f0a266511fc40f6e4.png)
,
odnosno, jedine takve funkcije su
![](https://static.elitesecurity.org/tex/32fbdf6a3f5e0ae2a5840ec49ebd32d8.png)
i
![](https://static.elitesecurity.org/tex/a18b01df1c6ea32270c636076d4b640d.png)
, odnosno
![](https://static.elitesecurity.org/tex/c89e4ae4d3b7201d62b6fc9a85699e8d.png)
i
![](https://static.elitesecurity.org/tex/0c002772b77ffa5462532891ce1df05e.png)
.
Nije bitno koji su zaključci izvučeni, već kako se do njih došlo.