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11th Grade Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 2 — Answers

Answer sheet with worked solutions for the 11th Grade functions worksheet.

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11th Grade 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.Find the inverse function of f(x) = −2x − 6.

Answer: f−1(x) =

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

Answer: 10x + 3

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

Answer: x − 5

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

Answer: −20x + 22

  1. f(g(x)) = −4(5x − 4) + 6
  2. = −20x + 22
5.Find the inverse function of f(x) = 3x − 9.

Answer: f−1(x) =

  1. y = 3x − 9
  2. Swap x and y: x = 3y − 9
  3. Solve for y: y =
6.f(x) = 4x − 5 and g(x) = 4x. Find g(f(x)) in simplest form.

Answer: 16x − 20

  1. g(f(x)) = 4(4x − 5)
  2. = 16x − 20
7.Find the inverse function of f(x) = 7x + 7.

Answer: f−1(x) =

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

Answer: 20x − 23

  1. f(g(x)) = 5(4x − 5) + 2
  2. = 20x − 23
9.f(x) = −x and g(x) = 3x + 5. Find g(f(x)) in simplest form.

Answer: −3x + 5

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

Answer: −15x − 20

  1. g(f(x)) = 5(−3x − 3) − 5
  2. = −15x − 20
11.f(x) = 4x + 6 and g(x) = 2x − 2. Find g(f(x)) in simplest form.

Answer: 8x + 10

  1. g(f(x)) = 2(4x + 6) − 2
  2. = 8x + 10
12.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 =
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