R,
Example 4.1.2
PRACTICE EXERCISES
1. Define functions f
and g from R
to R by the formulas: for all x R,
f(x) = 
and
g(x) = 3x
Is f = g? Prove or disprove by giving counter example.
2. Find the exact values of the following
quantities. Do not use a calculator.
a. log31
b. log24k, k is any positive integer.
| 3. | Consider the three-place Boolean function f defined by the following rule: for each triple (x1, x2, x3) of 0's and 1's, |
f(x1, x2, x3) = (3x1 + x2 + 2x3) mod 2.
a. Find f(1, 0, 1) and f(0, 1, 1).
b. Describe f using an input/output
table
