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Year 13 Function Notation, Composites and Inverses Worksheet — Level 2 — Answers

Answer sheet with worked solutions for the Year 13 functions worksheet.

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Success TutoringWorksheetsAnswer sheetYear 13 · Mathematics · Functions

Year 13 Function Notation, Composites and Inverses Worksheet — Level 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.f(x) = 4x + 6 and g(x) = 4x − 3. Find f(g(x)) in simplest form.

Answer: 16x − 6

  1. f(g(x)) = 4(4x − 3) + 6
  2. = 16x − 6
2.f(x) = 4x − 4 and g(x) = −2x − 6. Find f(g(x)) in simplest form.

Answer: −8x − 28

  1. f(g(x)) = 4(−2x − 6) − 4
  2. = −8x − 28
3.If f(x) = x2, find f(4).

Answer: 16

  1. Replace x with 4: (4)2
  2. = 16
4.f(x) = −3x − 3 and g(x) = −3x + 1. Find g(f(x)) in simplest form.

Answer: 9x + 10

  1. g(f(x)) = −3(−3x − 3) + 1
  2. = 9x + 10
5.If f(x) = 3x2 + 5x + 8, find f(0).

Answer: 8

  1. Replace x with 0: 3(0)2 + 5(0) + 8
  2. = 8
6.If f(x) = x2 − 5x − 6, find f(−4).

Answer: 30

  1. Replace x with −4: (−4)2 − 5(−4) − 6
  2. = 30
7.If f(x) = x2 − 5x − 6, find f(5).

Answer: −6

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

Answer: −20x − 35

  1. f(g(x)) = 5(−4x − 6) − 5
  2. = −20x − 35
9.f(x) = 3x + 6 and g(x) = 2x + 4. Find g(f(x)) in simplest form.

Answer: 6x + 16

  1. g(f(x)) = 2(3x + 6) + 4
  2. = 6x + 16
10.If f(x) = 4x2 + x − 3, find f(0).

Answer: −3

  1. Replace x with 0: 4(0)2 + (0) − 3
  2. = −3
11.If f(x) = −2x2 − 2x − 1, find f(4).

Answer: −41

  1. Replace x with 4: −2(4)2 − 2(4) − 1
  2. = −41
12.If f(x) = 4x2 + 6x + 6, find f(2).

Answer: 34

  1. Replace x with 2: 4(2)2 + 6(2) + 6
  2. = 34
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