# Precalculus : Algebra of Functions

## Example Questions

### Example Question #6 : 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 #9 : 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 .

Explanation:

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

### Example Question #161 : Functions

Let

Determine .

Explanation:

To find the composite function we start from the most inner portion of the expression and work our way out.

### Example Question #162 : Functions

Let

Determine

.

Explanation:

The composite funtion means to replace every entry x in f(x) with the entire function g(x).

### Example Question #163 : Functions

For , , and , determine .

Explanation:

Working inside out, first do .

This is,

.

Now we will do .

This is

### Example Question #164 : Functions

For , write a function for .

Explanation:

Working from the inside out, first we will find a function for .

This is:

, which we can simplify slightly to .

Now we will plug this new function into the function k:

.

Since ln is the inverse of e to any power, this simplifies to .

### Example Question #1121 : Pre Calculus

Find given the following equations