Math 110
In Class Exercises, Section 4.1
Page 1 / 4
Function Composition
1) Given the following pair of functions:
f x   x 2  1
g x   x  5
find
a)  f  g x
b) g  f x
c)  f  g 3
d) g  f 3
Make sure that you can calculate these by first calculating the 'inner' function, then feeding that result into the outer
function, as well as by figuring out the formula of the composite function, and then calculating the result.
e) What is the domain of  f  g x ?
Math 110
e) What is the domain of g  f x ?
Page 1 / 4
Math 110
In Class Exercises, Section 4.1
Page 2 / 4
2) Given the following pair of functions:
2
f x  
x
g x   x 2  1
find
a)  f  g x
b) g  f x
c) What is the domain of  f  g x ?
d) What is the domain of g  f x ?
3) Given the function H, suggest functions f and g such that  f  g x is the same as H
H  x   3x  7 
3
Math 110
Page 2 / 4
Math 110
In Class Exercises, Section 4.1
Page 3 / 4
4) Given the function H, suggest functions f and g such that  f  g x is the same as H
H  x   3x  7
5) Given the function H, suggest functions f and g such that  f  g x is the same as H
H x   3 x3  2 x 2  3x  17
6) From your textbook, in section 4.1, do problem #63:
7) From your textbook, in section 4.1, do problem #64:
Math 110
Page 3 / 4
Math 110
In Class Exercises, Section 4.1
Page 4 / 4
X
Review: Average Rate Of Change (More Review)
Goal: Identify the rate of change of a function, given it's picture ; intuitively understand ARoC
8) What is the average rate of change
between x = -8 and x = 0?
10
9
8
7
6
5
4
3
2
1
0
-1 0 1
-1 -9 -8 -7 -6 -5 -4 -3 -2 -1
-2
0
-3
-4
-5
-6
-7
-8
-9
-10
Y
Draw the secant line between these
two points on the graph to the left
2 3 4 5 6 7 8 9 10
What is the average rate of change
between x = 2 and x = 3?
Draw the secant line between these
two points on the graph to the left
Assume that the above graph represents the spread of the flu. The x-axis represents time (in
days), with x = 0 representing the date of a rock concert that lots and lots of people attend. The yaxis represents the number of people (in thousands) that have been not only been infected with
this particular strain of the flu, but can infect other people.
What can you say about the average rate of change between 8 days prior to the concert, and the
date of the concert?
What can you say about the average rate of change between 2 and 3 days after the concert?
After the concert, how did the rate of change of the function (i.e., the speed at which people are
contracting this flu, and becoming contagious) change after the concert?
Math 110
Page 4 / 4