Problem 1--Solution

Our function is

.

This means that whatever number, or expression, we substitute for x, the function f squares it, multiplies by 3, and then subtracts the result from 1. Hence:

f(x)= 1- 3*2^2= -11, .

We substitute these into our difference quotient and obtain:

.

Of course, -(-11)=+11. We add it to 1 at the beginning of the numerator and obtain 12. The crucial step consists of expanding using the formula for the square of a sum. Recall the formula and expand our expression:

, .

We substitute the expanded expression into the quotient and obtain:

.

Now, we have to multiply the expression in parentheses by 3 and get rid of the parentheses. Remember: there is a minus sign in front of the parentheses!

.

We can factor h from both terms of the numerator and cancel with h in the denominator. We obtain the final answer:

.