Definition of Bijection, Injection, and Surjection

\(15\) football teams are competing in a knock-out tournament. Each game has a winner, there are no draws, and the losing team is out of the tournament. How many games need to be played in order for a tournament champion to be determined?

For two sets \[X=\{-1,1,a\}, Y=\{8,9, b\},\] \(f(x)=x^3+9\) is a bijective function from \(X\) to \(Y\). What is the value of \(a+b\)?

For the two sets \(X=\{a, b, c\}\) and \(Y=\{9, 17, 72\},\) how many bijective functions are there from \(X\) to \(Y\)?

Suppose \(f(x)=ax+3\) is a bijective function from \(\mathbb{R}\) to \(\mathbb{R}\). If \(f(7)=38,\) what value of \(x\) satisfies \(f(x) =103?\)

Suppose \(f(x)=ax+3\) is a bijective function from \(\mathbb{R}\) to \(\mathbb{R}\). If \(f(5)=28,\) what value of \(x\) satisfies \(f(x) =78?\)