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

Answer: 12x + 16

  1. f(g(x)) = 3(4x + 5) + 1
  2. = 12x + 16
4.f(x) = x − 5 and g(x) = 3x + 5. Find g(f(x)) in simplest form.

Answer: 3x − 10

  1. g(f(x)) = 3(x − 5) + 5
  2. = 3x − 10
5.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 =
6.f(x) = 5x − 4 and g(x) = −3x + 2. Find g(f(x)) in simplest form.

Answer: −15x + 14

  1. g(f(x)) = −3(5x − 4) + 2
  2. = −15x + 14
7.Find the inverse function of f(x) = x + 5.

Answer: f−1(x) = x − 5

  1. y = x + 5
  2. Swap x and y: x = y + 5
  3. Solve for y: y = x − 5
8.Find the inverse function of f(x) = 5x − 8.

Answer: f−1(x) =

  1. y = 5x − 8
  2. Swap x and y: x = 5y − 8
  3. Solve for y: y =
9.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
10.f(x) = 3x and g(x) = −2x + 2. Find f(g(x)) in simplest form.

Answer: −6x + 6

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

Answer: −2x + 9

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

Answer: −15x − 12

  1. g(f(x)) = −3(5x + 4)
  2. = −15x − 12
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