# Lesson Worksheet: Composite Functions Mathematics

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

**Q5: **

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

- Aall real numbers
- B
- C
- D
- E

**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

**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,

**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