Lesson 4-2Lesson 4-2Operations on FunctionsOperations on Functions

• We can do some basic operations on functions.

• We can do some basic operations on functions.

• We can add, subtract, multiply and divide functions.

If given functions f(x) and g(x):

If given functions f(x) and g(x):

The sum of functions f and g is

If given functions f(x) and g(x):

The sum of functions f and g is

If given functions f(x) and g(x):

The difference of functions f and g is

If given functions f(x) and g(x):

The difference of functions f and g is

If given functions f(x) and g(x):

The product of functions f and g is

If given functions f(x) and g(x):

The product of functions f and g is

If given functions f(x) and g(x):

The quotient of functions f and g is

Example:Let f(x) = x + 1 and g(x) = x2 – 1, find a rule for

each of the following functions.

Example:Let f(x) = x + 1 and g(x) = x2 – 1, find a rule for

each of the following functions.

Example:Let f(x) = x + 1 and g(x) = x2 – 1, find a rule for

each of the following functions.

• Another way of combining functions is called composition of functions.

• Another way of combining functions is called composition of functions.

• This is simply a process of substituting a functions rule in for the variable in a 2nd function.

Example:

Example:

Example:

Example:

Example:

Example:

Assignment:

Pgs. 127-129C. E. 1-13 all,

W.E. 1-19 odd