# Precalculus : Algebra of Functions

## Example Questions

### Example Question #1122 : Pre Calculus

If and , find

Explanation:

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 .

Explanation:

"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 .

Explanation:

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

### Example Question #1125 : Pre Calculus

Given  and , find .

Explanation:

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.

### Example Question #1126 : Pre Calculus

Given    and   , find .

Explanation:

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   .

Explanation:

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?

Explanation:

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.

### Example Question #23 : Composition Of Functions

Find  given

and

Explanation:

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

Then,  is

### Example Question #24 : Composition Of Functions

Find  given the following.

Explanation:

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: