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Year 12 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 4 — Answers

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Year 12 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 4 — 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) = −3x − 2 and g(x) = −3x − 5. Find f(g(x)) in simplest form.

Answer: 9x + 13

  1. f(g(x)) = −3(−3x − 5) − 2
  2. = 9x + 13
2.f(x) = −3x − 2 and g(x) = −x + 3. Find f(g(x)) in simplest form.

Answer: 3x − 11

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

Answer: −12x + 28

  1. f(g(x)) = −4(3x − 6) + 4
  2. = −12x + 28
4.f(x) = 4x + 6 and g(x) = 4x − 6. Find g(f(x)) in simplest form.

Answer: 16x + 18

  1. g(f(x)) = 4(4x + 6) − 6
  2. = 16x + 18
5.Find the inverse function of f(x) = 6x − 4.

Answer: f−1(x) =

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

Answer: 25x − 24

  1. g(f(x)) = 5(5x − 4) − 4
  2. = 25x − 24
7.Find the inverse function of f(x) = −3x − 3.

Answer: f−1(x) =

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

Answer: −6x − 8

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

Answer: f−1(x) = x − 8

  1. y = x + 8
  2. Swap x and y: x = y + 8
  3. Solve for y: y = x − 8
10.f(x) = 5x + 2 and g(x) = x + 1. Find f(g(x)) in simplest form.

Answer: 5x + 7

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

Answer: 8x + 12

  1. g(f(x)) = 2(4x + 5) + 2
  2. = 8x + 12
12.Find the inverse function of f(x) = −2x + 7.

Answer: f−1(x) =

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