CMSC 250 Fall 2001 Homework 10 solutions

1. 1. $n(x)\geq n(Y)$.

   2. $n(Y)\geq n(X)$.

   3. n(X)=1, since $n(X) = n(Y)$ (since $f$ is 1-1 and onto.

   4. $n(X) = n(Y)$ because $f$ must be 1-1 and onto.

2. 
   
   $$\frac{log_{5}3}{log_{5}4}= log_{4}3 = \frac{log_{2}3}{log_{2}4}.$$
   
   

3. 1 billion.

4. I have to pick out 20 marbles.

5. The inverse of $f(x)=x^3 + 2, x \in R$

   $x^3 +2= y$

   $x^3 = y-2$

   $x = \sqrt[3]{y-2}$

   $f^{-1}(y)= \sqrt[3]{y-2}$

6. Given, D $=\{0,1,2,3,4,5,6,7,8,9,10,11\}$

   1. (6x) mod 12.

   2. (x+3) mod 12.

   3. (x+6) mod 12.

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