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

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Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Functions

Year 12 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.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.f(x) = −x − 5 and g(x) = −3x − 2. Find f(g(x)) in simplest form.

Answer: 3x − 3

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

Answer: 4x + 14

  1. g(f(x)) = 4(x + 3) + 2
  2. = 4x + 14
4.Find the inverse function of f(x) = 2x − 1.

Answer: f−1(x) =

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

Answer: f−1(x) =

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

Answer: −4x + 9

  1. f(g(x)) = −1(4x − 3) + 6
  2. = −4x + 9
7.Find the inverse function of f(x) = x + 7.

Answer: f−1(x) = x − 7

  1. y = x + 7
  2. Swap x and y: x = y + 7
  3. Solve for y: y = x − 7
8.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 =
9.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 =
10.f(x) = −x − 3 and g(x) = 3x − 5. Find g(f(x)) in simplest form.

Answer: −3x − 14

  1. g(f(x)) = 3(−x − 3) − 5
  2. = −3x − 14
11.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
12.f(x) = 2x − 3 and g(x) = 4x + 5. Find g(f(x)) in simplest form.

Answer: 8x − 7

  1. g(f(x)) = 4(2x − 3) + 5
  2. = 8x − 7
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