Difference between revisions of "2017 UNM-PNM Statewide High School Mathematics Contest II Problems"
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==Problem 3== | ==Problem 3== | ||
− | Let <math>f(x) =\frac{x}{ | + | 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>. | (a) Determine <math>f\circ g(x)</math> and <math>g\circ f(x)</math>. | ||
− | (b) Denote <math>\ | + | (b) Denote <math>\underbrace{h\circ h\circ \cdot \circ h}_\text{n times} := h^n</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>. | + | 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>. |
[[2017 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 3|Solution]] | [[2017 UNM-PNM Statewide High School Mathematics Contest II Problems/Problem 3|Solution]] |
Revision as of 02:52, 15 January 2019
UNM - PNM STATEWIDE MATHEMATICS CONTEST XLIX. February 4, 2017. Second Round. Three Hours
Contents
Problem 1
What are the last two digits of ?
Problem 2
Suppose , and all denote distinct digits from to . If , what are , and ?
Problem 3
Let and .
(a) Determine and .
(b) Denote . Determine all the functions in the set or for some a whole number.