COMC Functions and Sequences

Question 1

A function f satisfies f(x + y) = f(x) + f(y) for all real numbers x and y, and f(1) = 4. What is f(7)?

Accepted Answer

28

Answer

21

Answer

24

Answer

32

Question 2

If f(2x) = f(x) + x for all x > 0 and f(1) = 0, what is f(8)?

Accepted Answer

7

Answer

5

Answer

6

Answer

8

Question 3

Let f(x) = ax + b with a > 0. If f(f(x)) = 9x + 16, what is a + b?

Accepted Answer

7

Answer

5

Answer

6

Answer

8

Question 4

How many functions f: {1, 2, 3} → {1, 2, 3} satisfy f(f(x)) = x for all x in the domain?

Accepted Answer

4

Answer

3

Answer

5

Answer

6

Question 5

The function f satisfies f(1) = 1 and f(n+1) = f(n) + 2n for all positive integers n. What is f(6)?

Accepted Answer

31

Answer

25

Answer

28

Answer

36

Question 6

Let g(x) = x² − 3 and f(x) = 2x + 1. For how many integer values of x does f(g(x)) = g(f(x))?

Accepted Answer

0

Answer

1

Answer

2

Answer

3

Question 7

A function f defined for positive reals satisfies f(x/y) = f(x) − f(y) for all x, y > 0, and f(4) = 2. What is f(64)?

Accepted Answer

6

Answer

4

Answer

5

Answer

8