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Year 12 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 3 — Answers

Answer sheet with worked solutions for the Year 12 functions worksheet.

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

Answer: 6x + 17

  1. g(f(x)) = −3(−2x − 6) − 1
  2. = 6x + 17
2.Find the inverse function of f(x) = 7x + 6.

Answer: f−1(x) =

  1. y = 7x + 6
  2. Swap x and y: x = 7y + 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.Find the inverse function of f(x) = 4x + 6.

Answer: f−1(x) =

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

Answer: x − 5

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

Answer: −12x + 8

  1. f(g(x)) = −4(3x − 3) − 4
  2. = −12x + 8
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) = −4x + 3 and g(x) = −3x + 5. Find g(f(x)) in simplest form.

Answer: 12x − 4

  1. g(f(x)) = −3(−4x + 3) + 5
  2. = 12x − 4
9.Find the inverse function of f(x) = 2x.

Answer: f−1(x) =

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

Answer: f−1(x) =

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

Answer: −12x − 15

  1. f(g(x)) = 4(−3x − 3) − 3
  2. = −12x − 15
12.f(x) = 4x − 4 and g(x) = 3x + 4. Find g(f(x)) in simplest form.

Answer: 12x − 8

  1. g(f(x)) = 3(4x − 4) + 4
  2. = 12x − 8
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