>>12206122x a number in a set. A set is like a bag full of card, the cards have numbers written on them.
the stuff inside the bag is all real numbers.
so we write "x is a number in the set of real numbers" short hand because we're lazy as "x ? R"
R is short had for "the set of real numbers"
x+1 describes a behavior of a function.
the function is denoted as f(x) short hand for "function of x"
= means "is"
"the function of x is x plus 1"
short hand: f(x) = x+1
f(x) can be thought of as a set too.
so imagine you have your bag of numbers.
add one to all those distinct numbers and then flip the card over and write that new number on it in a different color and then put them into a new bag "f(x)"
You can call this a mapping.
when x is 1: "x=1"
we can look at our new bag and check what f(x) value is associated with x being 1.
Because we're lazy we write this short had as f(1)
well recall the function
f(x) = x+1
instead of looking though that bag, which is a lot of work because there's a lot of number in it, we can just use the right side of the function x+1 and substitute where the "x" is with the number we want.
x=1
x+1 can now be written as (1)+1
f(1)=1+1
and 1+1 = 2
so
f(1) = 2
the function defined as x plus one when x is one is 2
{f(x)| x+1, x ?R}
this is the set of the function f(x)
the name if f(x)
the behavior is x+1
x is any real number
lets restart with a different function, say it's called j.
j(x) = 2x+5
what is the "function j(x) equal to when x = 1" (short hand: j(1)).
