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Year 12 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 2 — Answers

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

Answer: −8x − 9

  1. f(g(x)) = −2(4x + 2) − 5
  2. = −8x − 9
2.f(x) = 2x − 2 and g(x) = −2x − 4. Find g(f(x)) in simplest form.

Answer: −4x

  1. g(f(x)) = −2(2x − 2) − 4
  2. = −4x
3.Find the inverse function of f(x) = 6x − 3.

Answer: f−1(x) =

  1. y = 6x − 3
  2. Swap x and y: x = 6y − 3
  3. Solve for y: y =
4.Find the inverse function of f(x) = 6x − 7.

Answer: f−1(x) =

  1. y = 6x − 7
  2. Swap x and y: x = 6y − 7
  3. Solve for y: y =
5.f(x) = 3x + 3 and g(x) = x − 1. Find g(f(x)) in simplest form.

Answer: 3x + 2

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

Answer: −8x + 8

  1. f(g(x)) = −2(4x − 6) − 4
  2. = −8x + 8
7.Find the inverse function of f(x) = 5x − 9.

Answer: f−1(x) =

  1. y = 5x − 9
  2. Swap x and y: x = 5y − 9
  3. Solve for y: y =
8.Find the inverse function of f(x) = −4x.

Answer: f−1(x) = −

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

Answer: −8x + 18

  1. f(g(x)) = 4(−2x + 4) + 2
  2. = −8x + 18
10.Find the inverse function of f(x) = −4x + 2.

Answer: f−1(x) =

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

Answer: 4x − 6

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

Answer: 4x − 3

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