Success TutoringWorksheets

Year 11 Function Notation, Composites and Inverses Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the Year 11 functions worksheet.

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Functions

Year 11 Function Notation, Composites and Inverses Worksheet — Level 3 — Answers

f(x) notation means "the value of the function at x". For a composite, substitute the inner function into the outer one. For an inverse, swap x and y and solve for y.

1.f(x) = −x + 6 and g(x) = 5x + 5. Find g(f(x)) in simplest form.

Answer: −5x + 35

  1. g(f(x)) = 5(−x + 6) + 5
  2. = −5x + 35
2.f(x) = x + 3 and g(x) = −3x. Find g(f(x)) in simplest form.

Answer: −3x − 9

  1. g(f(x)) = −3(x + 3)
  2. = −3x − 9
3.Find the inverse function of f(x) = 7x + 9.

Answer: f−1(x) =

  1. y = 7x + 9
  2. Swap x and y: x = 7y + 9
  3. Solve for y: y =
4.Find the inverse function of f(x) = 4x.

Answer: f−1(x) =

  1. y = 4x
  2. Swap x and y: x = 4y
  3. Solve for y: y =
5.f(x) = x + 4 and g(x) = −2x + 4. Find f(g(x)) in simplest form.

Answer: −2x + 8

  1. f(g(x)) = 1(−2x + 4) + 4
  2. = −2x + 8
6.f(x) = 2x + 4 and g(x) = −4x + 3. Find f(g(x)) in simplest form.

Answer: −8x + 10

  1. f(g(x)) = 2(−4x + 3) + 4
  2. = −8x + 10
7.Find the inverse function of f(x) = 7x − 2.

Answer: f−1(x) =

  1. y = 7x − 2
  2. Swap x and y: x = 7y − 2
  3. Solve for y: y =
8.f(x) = 4x and g(x) = −x − 5. Find f(g(x)) in simplest form.

Answer: −4x − 20

  1. f(g(x)) = 4(−x − 5)
  2. = −4x − 20
9.Find the inverse function of f(x) = 2x + 4.

Answer: f−1(x) =

  1. y = 2x + 4
  2. Swap x and y: x = 2y + 4
  3. Solve for y: y =
10.f(x) = 3x + 6 and g(x) = 5x + 6. Find g(f(x)) in simplest form.

Answer: 15x + 36

  1. g(f(x)) = 5(3x + 6) + 6
  2. = 15x + 36
11.Find the inverse function of f(x) = −3x + 9.

Answer: f−1(x) =

  1. y = −3x + 9
  2. Swap x and y: x = −3y + 9
  3. Solve for y: y =
12.Find the inverse function of f(x) = −6x + 3.

Answer: f−1(x) =

  1. y = −6x + 3
  2. Swap x and y: x = −6y + 3
  3. Solve for y: y =
Free worksheets at worksheets.successtutoring.com · © Success Tutoring · Free for personal and classroom use

Marking tips

  • Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
  • For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
  • Celebrate what went well first, then pick one thing to work on next.

Great work. Here's what to try next: