# Algebra 1 : How to find f(x)

## Example Questions

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### Example Question #1 : Algebraic Functions

A function is given by .  Find .

Explanation:

Plugging in 2 wherever  is present in the formula yields an answer of 14.

### Example Question #2 : Algebraic Functions

If , evaluate .

Explanation:

To solve this function, we simply need to understand that finding   means that  in this specific case. So, we can just substitute 10 in for .

is equal to , so our final answer is

or .

### Example Question #3 : Algebraic Functions

In which of these relations is  not a function of  ?

Explanation:

In the relation , there are many values of  that can be paired with more than one value of  - for example, .

To demonstrate that   is a function of  in the other examples, we solve each for :

can be rewritten as .

can be rewritten as

can be rewritten as

need not be rewritten.

In each case, we see that for any value of  can be uniquely defined.

Explanation:

### Example Question #2 : How To Find F(X)

What is the next number in the following sequence?

Explanation:

To form this sequence, alternately multiply by 2 and add 5:

To keep the pattern going, double the seventh term to get the eighth:

### Example Question #6 : Algebraic Functions

Define  and

Evaluate

is undefined.

Explanation:

The easiest way to find  is to take advantage of the fact that the radical expressons are conjugates, and that their product follows the difference of squares pattern.

### Example Question #3 : How To Find F(X)

Define  and  .

Evaluate

is undefined.

is undefined.

Explanation:

The domain of  is the intersection of the domains of the functions  and . Both domains are restricted by the same radical expression; since it must hold that the common radicand  is positive:

or

is therefore outside of the domains of  and  and, subsequently, that of .

### Example Question #4 : How To Find F(X)

What is the next number in the following sequence:

Explanation:

To get each member of this sequence, add a number that increases by one with each element:

To get the next element, add 7:

### Example Question #5 : How To Find F(X)

If   , then what is   ?

Explanation:

Replace  with  in the definition, then simplify.

### Example Question #6 : How To Find F(X)

If   , then what is   ?