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

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

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Success TutoringWorksheetsAnswer sheetYear 11 · Mathematics · Functions

Year 11 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) = −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
2.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 =
3.Find the inverse function of f(x) = 5x + 3.

Answer: f−1(x) =

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

Answer: −3x − 19

  1. g(f(x)) = −3(x + 6) − 1
  2. = −3x − 19
5.f(x) = x + 3 and g(x) = 4x + 6. Find g(f(x)) in simplest form.

Answer: 4x + 18

  1. g(f(x)) = 4(x + 3) + 6
  2. = 4x + 18
6.f(x) = 2x + 6 and g(x) = −x − 6. Find g(f(x)) in simplest form.

Answer: −2x − 12

  1. g(f(x)) = −1(2x + 6) − 6
  2. = −2x − 12
7.f(x) = −2x + 1 and g(x) = 3x − 2. Find f(g(x)) in simplest form.

Answer: −6x + 5

  1. f(g(x)) = −2(3x − 2) + 1
  2. = −6x + 5
8.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 =
9.f(x) = 4x − 5 and g(x) = 5x + 5. Find f(g(x)) in simplest form.

Answer: 20x + 15

  1. f(g(x)) = 4(5x + 5) − 5
  2. = 20x + 15
10.f(x) = 2x − 2 and g(x) = −x + 2. Find f(g(x)) in simplest form.

Answer: −2x + 2

  1. f(g(x)) = 2(−x + 2) − 2
  2. = −2x + 2
11.f(x) = −4x − 5 and g(x) = 3x − 6. Find f(g(x)) in simplest form.

Answer: −12x + 19

  1. f(g(x)) = −4(3x − 6) − 5
  2. = −12x + 19
12.f(x) = 5x − 6 and g(x) = −3x. Find g(f(x)) in simplest form.

Answer: −15x + 18

  1. g(f(x)) = −3(5x − 6)
  2. = −15x + 18
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