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

For the function *f* (*x*) = *x*^{2} – *x*, 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,

b. Find

**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} :

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 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 + 3*h* +*h*^{2}.

This means that

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