Bijective Functions

         

Let XX and YY be the sets X={x12x4,x is an integer}Y={y4<y<a,y is an integer} \begin{aligned} X &= \{ x \mid -12 \leq x \leq 4, x \text{ is an integer} \} \\ Y &= \{ y \mid 4 < y < a, y \text{ is an integer} \} \end{aligned} for some integer aa. If there exists a bijective function from XX to YY, what is the value of a?a?

Consider the sets X={a,b,c,d},Y={7,13,19,25},X=\{a,b,c,d\}, Y=\{7, 13, 19,25\}, and let ff be a bijective function from XX to YY. If MM and mm are the maximum and minimum values of f(a)+f(b)f(a)+f(b), respectively, what is MmM-m?

For two sets X={x1x1},Y={y2y16},X=\{x \mid -1 \leq x \leq 1\}, Y=\{y \mid 2 \leq y \leq 16\}, a bijective function f:XYf: X \to Y is defined as f(x)=ax+bf(x)=ax+b, where a>0a > 0. What is abab?

For set A={5,3,8,18}A=\{-5, 3, 8, 18\}, how many functions from AA to AA are not bijective?

For two sets X={xx11},Y={yy121},X=\{x\mid x\geq 11\}, Y=\{y\mid y\geq 121\}, function f:XYf: X \to Y is defined as f(x)=x22x+a.f(x)=x^2-2x+a. If ff is a one-to-one, bijective function, what is the value of the constant aa?

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