Algebra 1 : How to find f(x)

Study concepts, example questions & explanations for Algebra 1

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Example Questions

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Example Question #1 : How To Find F(X)

A function is given by .  Find .

Possible Answers:

Correct answer:

Explanation:

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

Example Question #2 : Algebraic Functions

If , evaluate .

Possible Answers:

Correct answer:

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 #2 : How To Find F(X)

In which of these relations is  not a function of  ?

Possible Answers:

Correct answer:

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.

Example Question #4 : Algebraic Functions

  

Possible Answers:

Correct answer:

Explanation:

Example Question #5 : Algebraic Functions

What is the next number in the following sequence?

Possible Answers:

Correct answer:

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 

Possible Answers:

 is undefined.

Correct answer:

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 #7 : Algebraic Functions

Define  and  .

Evaluate 

Possible Answers:

 is undefined.

Correct answer:

 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 #3 : How To Find F(X)

What is the next number in the following sequence:

Possible Answers:

Correct answer:

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 #9 : Algebraic Functions

If   , then what is   ?

Possible Answers:

Correct answer:

Explanation:

Replace  with  in the definition, then simplify.

Example Question #10 : Algebraic Functions

If   , then what is   ?

 

Possible Answers:

Correct answer:

Explanation:

Replace  with  in the definition, then simplify.

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