Composition of functions worksheet answer key algebra 2

1.

2.

Using f (x) = x2 and g(x) = x + 2,
a) find (f o g)(x) and (g o f)(x), in that order.

Choose:

3.

Functions f (x) and g(x) are defined as shown in the tables at the right. Use the tables to:
a) determine the following functions, in the order listed:
(f o g)(2); (g o f)(3); (f o f)(4);

Choose:

4.

5.

6.

7.

8.

Given f (x) = x2,   g(x) = 2x  and   h(x) = x - 2.
a) find ((f o g) o h)(x) and (f o (g o h))(x), in that order.

Choose:

9.

Which of the following statements is ALWAYS true?

10.

Note: The notation [x] means the greatest integer not exceeding the value of x.

11.

The formula K(C) = C + 273 converts Celsius temperature to Kelvin.
The formula

a. Write a composite function that will convert Fahrenheit
temperature to Kelvin.

b. Convert the boiling point of water (212º F) to Kelvin.

c. Convert the freezing point of water (32º F) to Kelvin.

12.

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, f (x), to represent just the 5 bonus points.
b.  Write a function, g(x), to represent just the percent of increase.
c.  Explain the meaning of f (g(x)).
d.  Find f (g(75)).
e.  Explain the meaning of g(f (x)).
f.  Find g(f (75)).
g.  Does f (g(x)) = g(f (x)) in this problem?