# Worksheet: Inverse and Composite Functions

Q1:

Which of the following functions is NOT its own inverse?

• A
• B
• C
• D
• E

Q2:

Which of the following functions is NOT its own inverse?

• A
• B
• C
• D
• E

Q3:

Let . Determine which of the following functions is the inverse of by checking whether .

• A
• B
• C

Q4:

Determine and so that is an inverse function to by considering .

• A
• B
• C and
• D and
• E and

Q5:

Let . Solve to find an expression for .

• A
• B
• C
• D
• E

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.
• E

Let . 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
• Cno conditions on any of the numbers

Q6:

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.

Q7:

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

Q8:

Suppose is the inverse function to . Determine and by considering the composition .

• A
• B
• C
• D
• E