# Precalculus : Algebra of Functions

## Example Questions

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### Example Question #26 : Composition Of Functions

Suppose  and .  Find .

Explanation:

To find , you must subsititue  into the function, .

### Example Question #27 : Composition Of Functions

If  and , what is

Explanation:

First, we find  or  Then, find , or

### Example Question #28 : Composition Of Functions

Given   and   find .

None of these.

Explanation:

Finding  is the same as plugging in  into  much like one would find  for a function .

and

Insert g(x) into f(x) everywhere there is a variable in f(x):

### Example Question #29 : Composition Of Functions

We are given the following:

and .

Find:

Explanation:

Let's discuss what the problem is asking us to solve. The expression  (read as as "f of g of x") is the same as . In other words, we need to substitute  into

Substitute the equation of  for the variable in the given  function:

Next we need to FOIL the squared term and simplify:

FOIL means that we multiply terms in the following order: first, outer, inner, and last.

First:

Outer:

Inner:

Last:

When we combine like terms, we get the following:

Substitute this back into the equation and continue to simplify.

None of the answers are correct.

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