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Year 13 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 2 — Answers

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Year 13 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 2 — 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) = −4x − 4.

Answer: f−1(x) =

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

Answer: 5x − 20

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

Answer: f−1(x) =

  1. y = −5x + 9
  2. Swap x and y: x = −5y + 9
  3. Solve for y: y =
4.Find the inverse function of f(x) = −x − 1.

Answer: f−1(x) = −x − 1

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

Answer: −12x + 30

  1. g(f(x)) = 4(−3x + 6) + 6
  2. = −12x + 30
6.Find the inverse function of f(x) = 6x + 2.

Answer: f−1(x) =

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

Answer: 20x − 36

  1. g(f(x)) = 5(4x − 6) − 6
  2. = 20x − 36
8.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 =
9.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 =
10.Find the inverse function of f(x) = 2x + 9.

Answer: f−1(x) =

  1. y = 2x + 9
  2. Swap x and y: x = 2y + 9
  3. Solve for y: y =
11.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
12.f(x) = 2x + 5 and g(x) = 5x + 2. Find g(f(x)) in simplest form.

Answer: 10x + 27

  1. g(f(x)) = 5(2x + 5) + 2
  2. = 10x + 27
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