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Year 12 Function Notation, Composites and Inverses Worksheet — Level 2 — 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 2 — 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.If f(x) = −x2 − x − 2, find f(−2).

Answer: −4

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

Answer: 15x + 1

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

Answer: x − 1

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

Answer: 4x + 3

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

Answer: −4x − 5

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

Answer: 15x − 11

  1. g(f(x)) = 3(5x − 4) + 1
  2. = 15x − 11
7.f(x) = −3x + 5 and g(x) = x − 2. Find f(g(x)) in simplest form.

Answer: −3x + 11

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

Answer: 4x + 16

  1. f(g(x)) = −2(−2x − 5) + 6
  2. = 4x + 16
9.If f(x) = −2x2 − x + 8, find f(3).

Answer: −13

  1. Replace x with 3: −2(3)2 − (3) + 8
  2. = −13
10.f(x) = 5x + 1 and g(x) = 4x − 5. Find g(f(x)) in simplest form.

Answer: 20x − 1

  1. g(f(x)) = 4(5x + 1) − 5
  2. = 20x − 1
11.f(x) = 2x − 3 and g(x) = 2x − 6. Find f(g(x)) in simplest form.

Answer: 4x − 15

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

Answer: −16x − 5

  1. f(g(x)) = −4(4x + 1) − 1
  2. = −16x − 5
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