# Precalculus : Algebra of Functions

## Example Questions

### Example Question #1 : Add, Subtract, Multiply, And Divide Functions

Simplify the following expression:

Explanation:

To simplify the above expression, we must combine all like terms:

Integers:

Putting all of the above terms together, we simplify to:

### Example Question #12 : Algebra Of Functions

If  and , what is ?

Explanation:

Given the information in the above problem, we know that:

Factoring the resulting fraction, we get:

### Example Question #13 : Algebra Of Functions

Simplify the following:

Explanation:

To simplify the expression, distribute the negative into the second parentheses, and then combine like terms.

### Example Question #14 : Algebra Of Functions

Simplify the following completely:

Explanation:

To simlify adding polynomials, simply drop the parentheses and add like terms.

### Example Question #15 : Algebra Of Functions

Determine the sum of:

Explanation:

To add the numerators, the denominators must be common.

The least common denominator can be determined by multiplication.

Rewrite the fractions.

### Example Question #16 : Algebra Of Functions

Given  and ,

Complete the operation given by .

Explanation:

Given  and

Complete the operation given by .

Begin by realizing what this is asking. We need to combine our two functions in such a way that we find the difference between them.

When doing so remember to distribute the negative sign that is in front of  to each term within the polynomial.

So, by simplifying the expression, we get our answer to be:

### Example Question #17 : Algebra Of Functions

Given  and ,

Evaluate and simplify .

Explanation:

Given  and ,

Evaluate and simplify .

Begin by multiplying  by 2:

Next, add  to what we got above and combine like terms.

.

### Example Question #18 : Algebra Of Functions

Given  and , find .

Explanation:

Given  and , find .

To complete this problem, we need to recall FOIL. FOIL states to multiply the terms in each binomial together in the order of first, outer, inner, and last.

We have no like terms to combine, so our answer is:

### Example Question #19 : Algebra Of Functions

Determine

if

and

Explanation:

is defined as the sum of the two functions  and .

As such

Determine

if

and