Functions with new definitions

1. Functions with New
Definitions
This type of problem is
usually on every SAT.

2. • Using New Defintions
• For functions, especially those involving
more than one variable, a special symbol is
sometimes introduced and defined.
• These symbols generally have unusual
looking signs (◊, *, § ) so you won’t confuse
them with standard mathematical symbols.
• The key to these questions is to make sure
that you read the definition carefully.

3. A typical special symbol question might look
something like this:
where w, x, y and z are integers.
Substitute 2 for w, 3 for x,
4 for z, and 1 for y
(2)(1) – (3)(4) = 2 – 12 = -10

4. Another example:
For all numbers x and y, let be defined as
x > y
x > = y x2 + . 3xy
What is the value of
(2 >1) >3?
(2 >1) means let x = 2, y = 1
Using x2 + 3xy, (2 >1) = 22 + 3(2)(1) = 4 + 6 = 10
Then (2 >1) >3 becomes 10 >3 so x=10 and y = 3
Using x 2 + 3 xy , (10 3) = 102 + 3(10)(3)
=
+ =
100 90 190
>