What Are Some Ways To Use Function Notation?

The example below demonstrates some ways that function notation can be used.

For the function f (x) = x2x, answer each of the questions.

a. Find the value of f (2) .

Solution To find f (2),  we need to replace the x in the formula with 2,

f of 2 equals two squared minus 2 or 2

b. Find  f of 1 divided by z

Solution Although the input is not a number, we still evaluate the function by replacing the x with the input. In this case, we replace x with 1/z :

f of 1 over z equals the quantity 1 over z squared minus 1 over z

c. Find all values of x for which f (x) = 6.

Solution Instead of supplying the input to the function, the output is supplied instead. To solve this part, set the formula equal to 6 and solve for x.

We can check that these values are correct by putting them into the function:

d. Find f (2 + h).

Solution Replace x with 2 + h in the function,

The output has been simplified by noting that (2 + h)2 is multiplied by FOILing:

e. The expression The quantity f of 2 + h minus f of 2 all divided by h is called a difference quotient. Find the value of this difference quotient.

Solution In part a we found that f (2) = 2 and in part d we found that f (2 + h) = 2 + 3h +h2.

This means that

To complete the difference quotient, divide this expression by h: