Difference between revisions of "2017 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 3"
(Created page with " == Problem == Let <math>f(x)=\frac{x}{x-1}</math> and <math>g(x)=\frac{x}{3x-1}</math>. (a) Determine <math>f\circ g(x)</math> and <math>g\circ f(x)</math>. (b) Denote...") |
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Determine all the functions in the set <math>S = \{H | H = (g\circ f)^n\circ g</math> or <math>H = (f\circ g)^n\circ f</math> for some <math>n</math> a whole number<math>\}</math>. | Determine all the functions in the set <math>S = \{H | H = (g\circ f)^n\circ g</math> or <math>H = (f\circ g)^n\circ f</math> for some <math>n</math> a whole number<math>\}</math>. | ||
== Solution== | == Solution== | ||
| − | + | <math>S=\Big\{ \frac{x}{(2n+1)x-1} | n\in \mathbb{Z} \Big \} </math> | |
| − | |||
== See also == | == See also == | ||
Latest revision as of 03:58, 19 January 2019
Problem
Let 
and 
.
(a) Determine 
and 
.
(b) Denote 
.
Determine all the functions in the set 
or 
for some 
a whole number
.
Solution
See also
| 2017 UNM-PNM Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 2 |
Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNM-PNM Problems and Solutions | ||
