Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**1a2b3c2212****Member**- Registered: 2009-04-04
- Posts: 419

Suppose p is an integer such that p≥0 and q is a natural number. It is also defined that p mod q is the remainder when p is divided by q. For example, 4mod4= 0, 7mod4=3, 3mod4=3.

Given that A={0,1,2,3,4} and f:A->A is defined by f(x)=3x mod5.

a)Express the function f as a set of ordered pairs.

b)Find the range of f.

c) Explain whether f^-1 exists or not and find f^-1 if it exists.

*Last edited by 1a2b3c2212 (2011-06-29 17:38:59)*

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

4mod4= 0, 7mod4=0, 3mod4=0.

The last 2 are not correct. 7 mod 4 = 3 and 3 mod 4 = 3.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

Offline

**1a2b3c2212****Member**- Registered: 2009-04-04
- Posts: 419

woops typo

Offline

**gnitsuk****Member**- Registered: 2006-02-09
- Posts: 121

1) {(0,0),(1,3),(2,1),(3,4),(4,2)}

2) From above the range of f(x) is A. This is because the value of f(x) can take any of all of the values from A = {0,1,2,3,4}.

3)

You can verify this by multiplying each second element in every ordered pair by 2 and reducing modulo 5 and seeing that the answer in each case is the first element in the corresponding ordered pair.

2 is said to be the multiplicative inverse of 3 mod(5)

Offline

Pages: **1**