The sum f + g
 f  g x  f x  g x
This just says that to find the sum of two functions, add
them together. You should simplify by finding like terms.
f x   2 x  3
g x   4 x  1
2
3
f  g  2x  3  4x 1
2
3
 4x  2x  4
3
2
Combine like
terms & put in
descending
order
The difference f - g
 f  g x  f x  g x
To find the difference between two functions, subtract
the first from the second. CAUTION: Make sure you
distribute the – to each term of the second function. You
should simplify by combining like terms.
f x   2 x  3
2

g x   4 x  1
3

f  g  2x  3  4x  1
2
3
Distribute
negative
 2 x  3  4 x  1  4 x  2 x  2
2
3
3
2
The product f • g
 f  g x  f x g x
To find the product of two functions, put parenthesis
around them and multiply each term from the first
function to each term of the second function.
f x   2 x  3
g x   4 x  1
2

3


f  g  2x  3 4x  1
2
3
 8 x  2 x  12 x  3
5
2
3
FOIL
Good idea to put in
descending order
but not required.
The quotient f /g
f
f x 
 x  
g x 
g
To find the quotient of two functions, put the first one
over the second.
f x   2 x  3
2
f 2x  3
 3
g 4x 1
2
g x   4 x  1
3
Nothing more you could do
here. (If you can reduce
these you should).
So the first 4 operations on functions are
pretty straight forward.
The rules for the domain of functions would
apply to these combinations of functions as
well. The domain of the sum, difference or
product would be the numbers x in the
domains of both f and g.
For the quotient, you would also need to
exclude any numbers x that would make the
resulting denominator 0.
Acknowledgement
I wish to thank Shawna Haider from Salt Lake Community College, Utah
USA for her hard work in creating this PowerPoint.
www.slcc.edu
Shawna has kindly given permission for this resource to be downloaded
from www.mathxtc.com and for it to be modified to suit the Western
Australian Mathematics Curriculum.
Stephen Corcoran
Head of Mathematics
St Stephen’s School – Carramar
www.ststephens.wa.edu.au