# Precalculus : Composition of Functions

## Example Questions

### Example Question #1 : Composition Of Functions

Suppose and

What would  be?

Explanation:

Substitute  into the function  for .

Then it will become:

### Example Question #1 : 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 #5 : Composition Of Functions

For the functions

and

.

Evaluate the composite function

.

DNE

Explanation:

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

Therefore the composite function becomes,

### Example Question #1 : Composition Of Functions

If , and , what is ?

Explanation:

When doing a composition of functions such as this one, you must always remember to start with the innermost parentheses and work backward towards the outside.

So, to begin, we have

.

Now we move outward, getting

.

Finally, we move outward one more time, getting

.

### Example Question #7 : Composition Of Functions

Find  if  , and .

Explanation:

Solve for the value of .

Solve for the value of .

Solve for the value .

### Example Question #8 : Composition Of Functions

For the functions  and , evaluate the composite function

Explanation:

The composite function notation  means to swap the function  into  for every value of . Therefore:

### Example Question #1 : Composition Of Functions

For the functions  and , evaluate the composite function

Explanation:

The composite function notation  means to swap the function  into  for every value of . Therefore:

### Example Question #10 : Composition Of Functions

For the functions  and , evaluate the composite function .