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Year 11 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 4 — Answers

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

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Year 11 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 4 — 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) = 3x + 6.

Answer: f−1(x) =

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

Answer: 4x − 27

  1. f(g(x)) = 4(x − 6) − 3
  2. = 4x − 27
3.Find the inverse function of f(x) = 5x − 5.

Answer: f−1(x) =

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

Answer: 8x + 6

  1. g(f(x)) = 2(4x + 6) − 6
  2. = 8x + 6
5.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 =
6.Find the inverse function of f(x) = 2x − 5.

Answer: f−1(x) =

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

Answer: 12x − 17

  1. f(g(x)) = 4(3x − 5) + 3
  2. = 12x − 17
10.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 =
11.f(x) = 4x − 2 and g(x) = −2x + 2. Find f(g(x)) in simplest form.

Answer: −8x + 6

  1. f(g(x)) = 4(−2x + 2) − 2
  2. = −8x + 6
12.Find the inverse function of f(x) = 3x − 4.

Answer: f−1(x) =

  1. y = 3x − 4
  2. Swap x and y: x = 3y − 4
  3. Solve for y: y =
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