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Year 10 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 3 — Answers

Answer sheet with worked solutions for the Year 10 functions worksheet.

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Year 10 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.f(x) = 4x + 6 and g(x) = 4x + 2. Find f(g(x)) in simplest form.

Answer: 16x + 14

  1. f(g(x)) = 4(4x + 2) + 6
  2. = 16x + 14
2.Find the inverse function of f(x) = 6x + 6.

Answer: f−1(x) =

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

Answer: f−1(x) =

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

Answer: 3x + 1

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

Answer: f−1(x) =

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

Answer: 3x − 11

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

Answer: −15x − 10

  1. f(g(x)) = −3(5x + 5) + 5
  2. = −15x − 10
9.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
10.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 =
11.f(x) = −2x − 6 and g(x) = x − 2. Find g(f(x)) in simplest form.

Answer: −2x − 8

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

Answer: f−1(x) = −x − 3

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