Practice with
Composition of Functions
 Topic Index | Algebra2/Trig Index | Regents Exam Prep Center


Solve the following problems pertaining to
composite functions.

1.


Using and ,
find:  a. 
         b.
         c. 
         d. 

 

 

2.


Using and ,
   find and .

Are these two answers the same?  What does this information tell you about compositions?

 

 

3.

Given ,   , and ,
find   and  .
 
Are these two answers the same?  What does this information tell you about compositions?

 

 

4.
The notation [x] means the greatest integer not exceeding the value of x.
Given ,    ,   and  
find a.  (Look out for this one!)
       b. 
       c. 
       d. 
       e. 
Are the answers for parts c and d the same?

 

 

5. Given and  ,
find and  .

 

 

 

6.

   and  

For what value of k is ?

 

 

7.

      and  

      Find the domain of .

 

 

8.

Which of the following statements is ALWAYS true?  

Choose:




 

 

9.

The formula converts Celsius temperature to Kelvin.
The formula converts Fahrenheit temperature to Celsius.

a. Write a composite function that will convert Fahrenheit
    temperature to Kelvin.
b. Convert the boiling point of water (212º F) and the
    freezing point of water (32º F) to Kelvin. 

 

 

10.

A math test has a bonus question.  The directions simply state that if you answer the question correctly you will receive 5 bonus points and your test grade will be increased by 7% of your score.

Let x = test score before answering the bonus question. 

a.  Write a function, , to represent just the 5 bonus
     points.
b.  Write a function, , to represent just the percent
     of increase.
c.  Explain the meaning of
d.  Find
e.  Explain the meaning of
f.  Find
g.  Does in this problem?