### All Precalculus Resources

## Example Questions

### Example Question #1122 : Pre Calculus

If and , find .

**Possible Answers:**

**Correct answer:**

First, make sure that gf (range of g is a subset of the domain of f).

Since the g: and f: , gf and exists.

Plug in the output of , which is , as the input of .

Thus,

### Example Question #1123 : Pre Calculus

Find and evaluate at .

**Possible Answers:**

**Correct answer:**

"G of F of X" means substitute f(x) for the variable in g(x).

Foil the squared term and simplify:

First:

Outer:

Inner:

Last:

So

Now evaluate the composite function at the indicated value of x:

### Example Question #1124 : Pre Calculus

Find if and .

**Possible Answers:**

**Correct answer:**

Replace and substitute the value of into so that we are finding .

### Example Question #1125 : Pre Calculus

Given and , find .

**Possible Answers:**

**Correct answer:**

Given and , find .

Begin by breaking this into steps. I will begin by computing the step, because that will make the late steps much more manageable.

Next, take our answer to and plug it into .

So we are close to our final answer, but we still need to multiply by 3.

Making our answer 84.

### Example Question #1126 : Pre Calculus

Given and , find .

**Possible Answers:**

None of the other answers.

**Correct answer:**

and is read as "g of f of x" and is equivalent to plugging the function f(x) into the variables in the function g(x).

### Example Question #21 : Composition Of Functions

and . Find .

**Possible Answers:**

**Correct answer:**

and .

To find we plug in the function everywhere there is a variable in the function .

This is the composition of "f of g of x".

Foil the square and simplify:

### Example Question #22 : Composition Of Functions

If and , what must be?

**Possible Answers:**

**Correct answer:**

Evaluate the composite function first.

Solve for by substituting into the value for .

The value of will be replaced inside , which will become .

Evaluate .

The value of is . Add one to this value.

The answer is .

### Example Question #23 : Composition Of Functions

Find given

and

**Possible Answers:**

**Correct answer:**

To evaluate, first evaluate and then plug in that answer into . Thus,

Then, is

### Example Question #24 : Composition Of Functions

Find given the following.

**Possible Answers:**

**Correct answer:**

To solve, plug 1 into g and then your answer into f.

Thus,

Plugging in this value into our f function we get the final answer as follows.

### Example Question #25 : Composition Of Functions

Find given the following functions:

**Possible Answers:**

**Correct answer:**

To solve, simply plug in 2 into f and then the result into g.

Thus,