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11th Grade Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 3 — 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 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.Find the inverse function of f(x) = −3x − 2.

Answer: f−1(x) =

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

Answer: 8x − 29

  1. g(f(x)) = 4(2x − 6) − 5
  2. = 8x − 29
3.f(x) = 2x + 5 and g(x) = −2x − 3. Find g(f(x)) in simplest form.

Answer: −4x − 13

  1. g(f(x)) = −2(2x + 5) − 3
  2. = −4x − 13
4.Find the inverse function of f(x) = 2x − 1.

Answer: f−1(x) =

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

Answer: −8x

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

Answer: f−1(x) =

  1. y = 7x + 9
  2. Swap x and y: x = 7y + 9
  3. Solve for y: y =
7.Find the inverse function of f(x) = x + 6.

Answer: f−1(x) = x − 6

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

Answer: 4x − 11

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

Answer: 12x + 22

  1. f(g(x)) = −3(−4x − 6) + 4
  2. = 12x + 22
10.Find the inverse function of f(x) = 5x.

Answer: f−1(x) =

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

Answer: f−1(x) =

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

Answer: f−1(x) =

  1. y = 4x + 1
  2. Swap x and y: x = 4y + 1
  3. Solve for y: y =
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