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

**Q5: **

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

- A
- B all real numbers
- 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 patientβs 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 ?

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

**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?

- 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

**Q25: **

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.