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12th Grade Function Notation, Composites and Inverses Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the 12th Grade functions worksheet.

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12th Grade Function Notation, Composites and Inverses Worksheet — Level 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.f(x) = 3x + 6 and g(x) = −2x + 5. Find g(f(x)) in simplest form.

Answer: −6x − 7

  1. g(f(x)) = −2(3x + 6) + 5
  2. = −6x − 7
2.f(x) = 5x − 6 and g(x) = 3x + 4. Find f(g(x)) in simplest form.

Answer: 15x + 14

  1. f(g(x)) = 5(3x + 4) − 6
  2. = 15x + 14
3.Find the inverse function of f(x) = 2x − 5.

Answer: f−1(x) =

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

Answer: −6x − 17

  1. g(f(x)) = −3(2x + 4) − 5
  2. = −6x − 17
5.f(x) = x − 5 and g(x) = 4x. Find f(g(x)) in simplest form.

Answer: 4x − 5

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

Answer: f−1(x) =

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

Answer: 20x + 10

  1. g(f(x)) = 5(4x + 3) − 5
  2. = 20x + 10
8.f(x) = −4x − 3 and g(x) = −x − 1. Find f(g(x)) in simplest form.

Answer: 4x + 1

  1. f(g(x)) = −4(−x − 1) − 3
  2. = 4x + 1
9.Find the inverse function of f(x) = −4x + 8.

Answer: f−1(x) =

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

Answer: f−1(x) =

  1. y = 5x − 1
  2. Swap x and y: x = 5y − 1
  3. Solve for y: y =
11.Find the inverse function of f(x) = −6x − 5.

Answer: f−1(x) =

  1. y = −6x − 5
  2. Swap x and y: x = −6y − 5
  3. Solve for y: y =
12.Find the inverse function of f(x) = −x − 3.

Answer: f−1(x) = −x − 3

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