# Lesson Worksheet: Composite Functions Mathematics

In this worksheet, we will practice forming a composite function by composing two or more 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:

If and , what is the coefficient of in ?

• A
• B
• C
• D
• E

Q11:

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

Q12:

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

• A, ,
• B, ,
• C, ,
• D, ,

Q13:

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

• A,
• B,
• C,
• D,
• E,

Q14:

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

• A
• B
• C
• D
• E

Q15:

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

Q16:

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,

Q17:

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

• A
• B
• C
• D
• E

Q18:

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

• A
• B
• C
• D
• E

Q19:

If , and , find the domain of .

• A
• B
• C
• D

Q20:

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

• A,
• B,
• C,
• D,

Q21:

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

• A
• B
• C
• D
• E

Q22:

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

Q23:

Suppose and . If is expressed in the form , determine the numbers and .

• A,
• B,
• C,
• D,
• E,

Q24:

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

• A,
• B,
• C,
• D,

Q25:

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

• A
• B
• C
• D