Definition of Bijection, Injection, and Surjection

         

1515 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},X=\{-1,1,a\}, Y=\{8,9, b\}, f(x)=x3+9f(x)=x^3+9 is a bijective function from XX to YY. What is the value of a+ba+b?

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

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

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

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