Algebra
# Functions

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

$a \leq f(x).$

What is the value of $a$?

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

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