Difference between revisions of "G285 2021 Summer Problem Set Problem 2"
Geometry285 (talk | contribs) (Created page with "==Problem== Let <cmath>f(x,y) = \begin{cases}x^y & \text{ if } x^2>y \text{ and } |x|<y\\f(f(\sqrt{|x|},y),y) & \text{ otherwise} \end{cases}</cmath> If <math>y</math> is a po...") |
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==Solution== | ==Solution== | ||
| − | Note for <math>x \in \{-1,1 \}</math>, our function approaches an infinite recursion. Now, for <math>-1<x<1</math>, we have the function approaches <math>-1</math>, or <math>1</math>, which also is an infinite recursion. The answer is <math>\boxed{\textbf{(C)}\ 0}</math> | + | Note for <math>x \in \{ -1,1 \}</math>, our function approaches an infinite recursion. Now, for <math>-1<x<1</math>, we have the function approaches <math>-1</math>, or <math>1</math>, which also is an infinite recursion. The answer is <math>\boxed{\textbf{(C)}\ 0}</math> |
Latest revision as of 22:15, 28 June 2021
Problem
Let ![\[f(x,y) = \begin{cases}x^y & \text{ if } x^2>y \text{ and } |x|<y\\f(f(\sqrt{|x|},y),y) & \text{ otherwise} \end{cases}\]](http://latex.artofproblemsolving.com/a/f/e/afea61bbc7bbc2d72748d6750aa5252ac6dd978a.png)
If 
is a positive integer, find the sum of all values of 
such that 
for some constant 
.
Solution
Note for 
, our function approaches an infinite recursion. Now, for 
, we have the function approaches 
, or 
, which also is an infinite recursion. The answer is 
