# Worksheet: Composite Functions

Q1:

Given and , find .

Q2:

Given that the function and the function , determine in its simplest form, and evaluate .

• A ,
• B ,
• C ,
• D ,

Q3:

If and , find .

Q4:

Given that the function , and the function , determine in its simplest form, and find its domain.

• A , domain
• B , domain
• C , domain
• D , domain
• E , domain

Q5:

Given that the function , and the function , find in its simplest form, then determine .

• A ,
• B ,
• C ,
• D ,
• E ,

Q6:

Given that the function , and the function , express in its simplest form, and find its domain, then evaluate .

• A , domain,
• B , domain,
• C , domain,
• D , domain,
• E , domain,

Q7:

For and , express in the form with suitable numbers for and .

• A
• B
• C
• D
• E

Q8:

Let . Which of the following functions are the correct and , if ?

• A ,
• B ,
• C ,
• D ,

Q9:

Let be one-to-one and onto, and let be one-to-one. What is the most that can be said about ?

• AThe image of and the image of are the same.
• B and are inverses.
• C is onto.
• D is one-to-one.

Q10:

An oil spill grows with time such that the shape resulting remains the same but has an increasing diameter . If the area of the spill is given by as a function of the diameter, and the diameter is given by as a function of time , what does represent?

• A the area of the spill as a function of the radius
• B the area of the spill as a function of time
• C the area of the spill as a function of the diameter
• D It does not represent anything.
• Ethe area of the spill multipled by the diameter

Q11:

Let and be maps. Which of the following statements is true?

• AThe domain of is .
• B and are inverses.
• C
• DIf is , then and are both onto.

Q12:

Given that the function , the function , and the function , determine , , and .

• A , ,
• B , ,
• C , ,
• D , ,

Q13:

If the function , and the function , find the domain of .

• A
• B
• C
• D
• E

Q14:

If the function , where , and the function , determine the domain of .

• A
• B
• C
• D
• E

Q15:

If , and , find the domain of .

• A
• B
• C
• D

Q16:

If and , then .

• A
• B
• C
• D

Q17:

Given , , and , evaluate .

Q18:

If the function and the function , find an expression for in its simplest form and determine its domain.

• A ,
• B ,
• C ,
• D ,

Q19:

Let , , and and suppose that , , , , , and . Which of the following represents ?

• A
• B
• C
• D

Q20:

Given and , evaluate .

• A25
• B125
• C1
• D100

Q21:

If the function , where , and the function , determine the domain of .

• A
• B
• C
• D
• E

Q22:

Suppose that and .

Find .

• A
• B
• C
• D
• E

Given that , find in terms of and .

• A
• B
• C
• D
• E

Q23:

Suppose that and . Find, in the simplest form, and .

• A ,
• B ,
• C ,
• D ,
• E ,

Q24:

If the function , and the function , find in the simplest form.

• A
• B
• C
• D

Q25:

Which of the following pairs of functions , satisfy ?

• A ,
• B ,
• C ,
• D ,