# Worksheet: Composite Functions

In this worksheet, we will practice forming a composite function by composing two or more linear, quadratic, exponential, or radical functions.

Q1:

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

• A,
• B,
• C,
• D,

Q2:

If and , find .

Q3:

Given and , which of the following expressions gives ?

• A
• B
• C
• D
• E

Q4:

Given and , find .

Q5:

Let and . For what values of is it true that ?

• Aall real numbers
• B
• C
• D
• E

Q6:

If and , find .

Q7:

If and , what is ?

• A
• B
• C
• D
• E

Q8:

Given that , find so that satisfies .

Q9:

Given that and , find and simplify an expression for .

• A
• B
• C
• D

Q10:

The function gives the pain level on a scale of 0 to 10 experienced by a patient with milligrams of a pain-reducing drug in their system. The number of milligrams of the drug in the patient’s system after minutes is modeled by . Which of the following would you do in order to determine when the patient will be at a pain level of 4?

• AEvaluating
• BEvaluating
• CSolving
• DSolving

Q11:

If and , what is the coefficient of in ?

• A
• B
• C
• D
• E

Q12:

In the given figure, the red graph represents , while the blue represents . What is ?

Q13:

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

• A, ,
• B, ,
• C, ,
• D, ,

Q14:

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

• A,
• B,
• C,
• D,
• E,

Q15:

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

• A
• B
• C
• D
• E

Q16:

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

Q17:

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,

Q18:

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

• A
• B
• C
• D
• E

Q19:

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

• A
• B
• C
• D
• E

Q20:

If , and , find the domain of .

• A
• B
• C
• D

Q21:

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

• A,
• B,
• C,
• D,

Q22:

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

• A
• B
• C
• D
• E

Q23:

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

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

Q24:

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?

• AIt does not represent anything.
• Bthe area of the spill multipled by the diameter
• Cthe area of the spill as a function of the radius
• Dthe area of the spill as a function of time
• Ethe area of the spill as a function of the diameter

Q25:

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

• A and are inverses.
• BThe domain of is .
• C
• DIf is , then and are both onto.