What Is Function Notation?

Function notation looks complicated, but it’s really just a different way of writing an equation. For example:
y = 3x + 2
f(x) = 3x + 2

both mean the same thing. When x is 6, y is 20 and f(6) is 20. f(6) just means ‘substitute 6 for x in the equation’. A few more examples:
f(x) = 4x - 5       => f(6) = 28 - 5 = 23
f(x) = 100 - 2x     => f(15) = 100 - 30 = 70
f(x) = x2 + x - 8   => f(2) = 4 + 2 - 8 = -2

As always, you need to be careful when there are negatives around:
f(x) = 3x - 2    => f(-3) = -9 - 2 = -11
f(x) = 20 - 5x   => f(-5) = 20 + 25 = 45
f(x) = 2x - x2   => f(-4) = -8 - 16 = -24
(Remember that the square of a negative is positive)

A common type of question is:
f(x) = 3x + 2
If f(t) = 17, find t

This is really another way of saying
If y = 3t + 2
find t when y = 17

The solution using function notation is to substitute the letter in the brackets (in this case ‘t’) for x in the equation. Then set it to the answer you were given and use algebra to find t.
f(x) = 3x + 2
If f(t) = 17, find t
f(t) = 3t + 2 = 17
3t + 2 = 17
3t = 15
t = 5

In the exam, they usually throw in some negatives:
f(x) = 16 - 4t
If f(t) = 24, find t
f(t) = 16 - 4t = 24
16 - 4t = 24
-4t = 8
t = -2