4.4 Notes.notebook 1 February 21, 2013 Mar 201:53 PM 4.4 Restrictions on Composite Functions If the domain of 2 functions is then the domain of their composition will be the same and have no restrictions. Ex) Look at f(x)=2x1 g(x)=x 2 1 and f(g(x)). Notice that the LEFT screen has been set so that only the composite function is displayed. What is the equation of f(g(x))? Notice its domain? __________________ What is the range of f(x), of g(x)? How would we find the range of f(g(x))?
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
4.4 Notes.notebook
1
February 21, 2013
Mar 201:53 PM
4.4 Restrictions on Composite Functions
If the domain of 2 functions is then the domain of their composition will be the sameand have no restrictions.
Ex) Look at f(x)=2x1 g(x)=x21 and f(g(x)).
Notice that the LEFT screen has been set so that onlythe composite function is displayed.What is the equation of f(g(x))? Notice its domain?
__________________What is the range of f(x), of g(x)?How would we find the range of f(g(x))?
4.4 Notes.notebook
2
February 21, 2013
Mar 202:04 PM
Use the same 2 equations to find the equation for g(g(x))Again, notice its domain is ALL inclusive.
Use your calculator to find the range of this function.Your screen should look like this:
4.4 Notes.notebook
3
February 21, 2013
Mar 202:08 PM
So far we conclude that if the domains of functions areall inclusive, so is the domain of their composite.
The range is more difficult to determine and might requirethe help of a calculator.
What if the domains of the original functions are NOT allinclusive. What about the composite function's domain??
4.4 Notes.notebook
4
February 21, 2013
Mar 202:10 PM
If and g(x) = x+3
state the domain of both f(x) and g(x) and find the domainof:
1) f(g(x)) Hint: Find the composite function and then determineits domain.
2) g(f(x))
4.4 Notes.notebook
5
February 21, 2013
Mar 202:17 PM
Remember, domains are restricted by NonPermissible Values. Denominators must NOT equal 0.
4.4 Notes.notebook
6
February 21, 2013
Mar 202:17 PM
4.4 Notes.notebook
7
February 21, 2013
Mar 202:19 PM
In this case, compose the function and then remember that Square Root functions only exist for positive values. This will determine the restrictions on the domain.
4.4 Notes.notebook
8
February 21, 2013
Mar 202:19 PM
Now try these:
This one has issues! The square root disappears inthe composition, but since the domain of f(x) is restricted,so is the domain of g(f(x)). Be careful.
4.4 Notes.notebook
9
February 21, 2013
Mar 202:14 PM
Now let's get creative.The final type of question GIVES the composite functionand asks for the original functions that would produce thiscomposition. Obviously in many cases, more than one answerwill work.