In this worksheet, we will practice using compositions of functions to find and justify inverses of functions.
Suppose is the inverse function to . Determine and by considering the composition .
Determine and so that is an inverse function to by considering .
- C and
- D and
- E and
Shown are the graphs of functions and g from the set into itself. Write the function as a list of ordered pairs. What can you conclude?
- A , is the inverse of
- B , is the inverse of
- C , is the inverse of
- D , is the inverse of
- E , is the inverse of
Let . Solve to find an expression for .
Find and when and .
- A ,
- B ,
- C ,
- D ,
- E ,
Let and . By considering the simplification of , what, if any, is the relation between and ?
- AThere is no relation between them.
- BThey are the same.
- CThey are inverses of each other.
- DThey are negatives of each other.
Let , and . By considering the simplifications of and , what, if any, are the relations between these functions?
- AThey are all the same.
- BThere is no relation between them.
- C is the inverse of .
- D is the negative of , and is twice .
Suppose that , where . What must be true of , , , and ?
- A , no conditions on and
- B , , , and
- Cno conditions on any of the numbers
Which of the following is a necessary condition for a function to be invertible?
- A has to be one-to-one.
- B has to be onto.
- C has to be a function.
- D has to be both one-to-one and onto.