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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 and g(x) = 5x + 4. Find g(f(x)) in simplest form.

Answer: −20x + 4

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

Answer: f−1(x) =

  1. y = 4x − 9
  2. Swap x and y: x = 4y − 9
  3. Solve for y: y =
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) = 5x + 1.

Answer: f−1(x) =

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

Answer: f−1(x) = −x − 4

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

Answer: 3x − 6

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

Answer: f−1(x) =

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

Answer: −2x − 12

  1. g(f(x)) = 2(−x − 4) − 4
  2. = −2x − 12
12.f(x) = 2x − 6 and g(x) = 2x. Find g(f(x)) in simplest form.

Answer: 4x − 12

  1. g(f(x)) = 2(2x − 6)
  2. = 4x − 12
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