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Year 12 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 2 — 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 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) = 5x − 5.

Answer: f−1(x) =

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

Answer: −4x + 2

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

Answer: −12x − 11

  1. f(g(x)) = −3(4x + 3) − 2
  2. = −12x − 11
4.f(x) = −x − 4 and g(x) = −x − 6. Find f(g(x)) in simplest form.

Answer: x + 2

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

Answer: −15x + 18

  1. f(g(x)) = 5(−3x + 3) + 3
  2. = −15x + 18
6.f(x) = −x − 3 and g(x) = 4x + 1. Find g(f(x)) in simplest form.

Answer: −4x − 11

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

Answer: 12x − 21

  1. g(f(x)) = 4(3x − 5) − 1
  2. = 12x − 21
8.f(x) = x − 3 and g(x) = 2x − 4. Find f(g(x)) in simplest form.

Answer: 2x − 7

  1. f(g(x)) = 1(2x − 4) − 3
  2. = 2x − 7
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) = 7x + 8.

Answer: f−1(x) =

  1. y = 7x + 8
  2. Swap x and y: x = 7y + 8
  3. Solve for y: y =
11.Find the inverse function of f(x) = −3x + 4.

Answer: f−1(x) =

  1. y = −3x + 4
  2. Swap x and y: x = −3y + 4
  3. Solve for y: y =
12.Find the inverse function of f(x) = 7x − 1.

Answer: f−1(x) =

  1. y = 7x − 1
  2. Swap x and y: x = 7y − 1
  3. Solve for y: y =
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