# Precalculus : Algebra of Functions

## Example Questions

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### Example Question #26 : Composition Of Functions

Suppose and .  Find .

Possible Answers:     Correct answer: Explanation:

To find , you must subsititue into the function, .    ### Example Question #27 : Composition Of Functions

If and , what is Possible Answers:    Correct answer: Explanation:

First, we find or Then, find , or ### Example Question #28 : Composition Of Functions

Given and find .

Possible Answers:  None of these.  Correct answer: 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: Possible Answers:

None of the other answers.    Correct answer:

None of the other answers.

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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