# Precalculus : Algebra of Functions

## Example Questions

### Example Question #11 : Add, Subtract, Multiply, And Divide Functions

Add the following functions:

Explanation:

To add, simply combine like terms. Thus, the answer is:

### Example Question #12 : Add, Subtract, Multiply, And Divide Functions

Given the functions:   and , what is ?

Explanation:

For , substitute the value of  inside the function for  and evaluate.

For , substitute the value of  inside the function for  and evaluate.

Subtract .

### Example Question #13 : Add, Subtract, Multiply, And Divide Functions

Simplify  given,

Explanation:

To solve , simply multiply your two functions. Thus,

### Example Question #21 : Add, Subtract, Multiply, And Divide Functions

If and , find .

Explanation:

To solve this problem, you must plug in the g function to wherever you see x in the f function. When you plug that in, it looks like this: . Then simplify so that your answer is: .

### Example Question #22 : Add, Subtract, Multiply, And Divide Functions

Find given    and  .

The answer is not present.

Explanation:

The problem is asking to find the composite function that results when f(x) is divided by g(x).

When dividing fractions, it is important to remember to multiply by the inverse.

Cross cancel the exponents leaving only one "x" in the bottom.

### Example Question #1 : Composition Of Functions

Suppose and

What would  be?

Explanation:

Substitute  into the function  for .

Then it will become:

### Example Question #2 : Composition Of Functions

What is ?

Explanation:

f(g(x)) simply means: where ever you see an x in the equation f(x), replace it with g(x).

So, doing just that, we get

,

which simplifies to

.

Since

our simplified expression becomes,

.

### Example Question #3 : Composition Of Functions

What is ?

Explanation:

g(f(x)) simply means replacing every x in g(x) with f(x).

After simplifying, it becomes

### Example Question #4 : Composition Of Functions

For the functions

and

.

Evaluate the composite function

.

DNE

Explanation:

The composite function means to plug in the function of  into the function  for every x value in the function.

Therefore the composition function becomes:

.

### Example Question #1 : Composition Of Functions

For the functions

and

.

Evaluate the composite function

.