Function Terminology


If we have a real-valued function f(x)=x2+27 f(x) = x^2 + 27 , the values of f(x) f(x) will necessarily fall in the following range:

af(x). a \leq f(x).

What is the value of a a ?

Consider two sets: X={a,b,c,d}, Y={1,2,3}. X = \{ a, b, c, d \}, \ Y = \{ 1, 2, 3 \}.

If a function is defined from X X to Y Y , what is the maximum possible number of such functions?

For two sets X={a,b,c},Y={7,11,13,17,20,32},X=\{a,b,c\}, Y=\{7, 11, 13, 17, 20, 32\}, ff is an injective function from XX to YY. If f(a)=7f(a)=7 and f(b)=17f(b)=17, what is the sum of all the elements of YY that can possibly be the value of f(c)f(c)?

Given that the domain and codomain of the function y=169x2y=\sqrt{169-x^2} are restricted to the real numbers, how many elements of the domain of y=169x2y=\sqrt{169-x^2} are integers?

For two sets X={1,1,a},Y={3,4,b},X=\{-1,1,a\}, Y=\{3,4, b\}, f(x)=x3+4f(x)=x^3+4 is a bijective function from XX to YY. What is the value of a+ba+b?


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