Success TutoringWorksheets

Year 12 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 3 — Answers

Answer sheet with worked solutions for the Year 12 functions worksheet.

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Functions

Year 12 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 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.Find the inverse function of f(x) = −2x + 3.

Answer: f−1(x) =

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

Answer: f−1(x) =

  1. y = −4x + 4
  2. Swap x and y: x = −4y + 4
  3. Solve for y: y =
3.Find the inverse function of f(x) = −5x + 6.

Answer: f−1(x) =

  1. y = −5x + 6
  2. Swap x and y: x = −5y + 6
  3. Solve for y: y =
4.Find the inverse function of f(x) = 4x − 3.

Answer: f−1(x) =

  1. y = 4x − 3
  2. Swap x and y: x = 4y − 3
  3. Solve for y: y =
5.Find the inverse function of f(x) = 7x − 5.

Answer: f−1(x) =

  1. y = 7x − 5
  2. Swap x and y: x = 7y − 5
  3. Solve for y: y =
6.Find the inverse function of f(x) = 6x − 8.

Answer: f−1(x) =

  1. y = 6x − 8
  2. Swap x and y: x = 6y − 8
  3. Solve for y: y =
7.f(x) = −3x + 2 and g(x) = 2x + 6. Find f(g(x)) in simplest form.

Answer: −6x − 16

  1. f(g(x)) = −3(2x + 6) + 2
  2. = −6x − 16
8.f(x) = −4x + 5 and g(x) = −x + 6. Find f(g(x)) in simplest form.

Answer: 4x − 19

  1. f(g(x)) = −4(−x + 6) + 5
  2. = 4x − 19
9.Find the inverse function of f(x) = 4x + 5.

Answer: f−1(x) =

  1. y = 4x + 5
  2. Swap x and y: x = 4y + 5
  3. Solve for y: y =
10.Find the inverse function of f(x) = −x − 6.

Answer: f−1(x) = −x − 6

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

Answer: −x + 1

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

Answer: f−1(x) =

  1. y = 4x + 7
  2. Swap x and y: x = 4y + 7
  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: