### All Precalculus Resources

## Example Questions

### Example Question #1 : Composition Of Functions

Suppose and

What would be?

**Possible Answers:**

**Correct answer:**

Substitute into the function for .

Then it will become:

### Example Question #2 : Composition Of Functions

What is ?

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

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

.

**Possible Answers:**

DNE

**Correct answer:**

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

.

**Possible Answers:**

DNE

**Correct answer:**

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

Therefore the composite function becomes,

### Example Question #5 : Composition Of Functions

If , , and , what is ?

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

**Correct answer:**

Solve for the value of .

Solve for the value of .

Solve for the value .

### Example Question #6 : Composition Of Functions

For the functions and , evaluate the composite function

**Possible Answers:**

**Correct answer:**

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

### Example Question #7 : Composition Of Functions

For the functions and , evaluate the composite function .

**Possible Answers:**

**Correct answer:**

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 .

**Possible Answers:**

None of the answers listed

**Correct answer:**

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