English | Español

Try our Free Online Math Solver!

Online Math Solver

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


Composition of Functions

Composition of the function f with the function g, given by , is defined by:

Domain of consists of all x in domain of g such that is in the domain of f.

Example. :If and , find:

Example: Use the graphs of f and g to evaluate each expression.

Example: In the example above, for what value (s) of x is ?

Horizontal Compression and Elongation of Graphs . If ,
a) For any constant , the graph of is the same as that of with a
change in the horizontal scale.

1) If horizontal compression

2) If horizontal elongation
b) The graph of is a reflection about the y-axis of the graph of .

1) For horizontal compression and reflection.

2) For horizontal elongation and reflection.

Example: Graph the following functions:

Example: If , , and , find:

Example: Use the graph of the function given below to sketch the graph of the indicated
functions.

Example: Write the function as the composition of three functions.


Applied Example: The number of bacteria in a refrigerated food is given by
where t is the Celsius temperature of the food. when
the food is removed from refrigeration , the temperature is given by
where t is the time in hours.

a) What does the composite function represent?

b) How many bacteria are in the food when t=2 hours?

Prev Next