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12th Grade Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 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 — 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.f(x) = 5x + 3 and g(x) = 4x − 2. Find f(g(x)) in simplest form.

Answer: 20x − 7

  1. f(g(x)) = 5(4x − 2) + 3
  2. = 20x − 7
2.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 =
3.f(x) = −2x + 4 and g(x) = 5x − 4. Find g(f(x)) in simplest form.

Answer: −10x + 16

  1. g(f(x)) = 5(−2x + 4) − 4
  2. = −10x + 16
4.f(x) = −3x and g(x) = −2x + 4. Find g(f(x)) in simplest form.

Answer: 6x + 4

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

Answer: −20x + 22

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

Answer: f−1(x) =

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

Answer: 5x − 1

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

Answer: −6x + 10

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

Answer: f−1(x) =

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

Answer: f−1(x) = x + 7

  1. y = x − 7
  2. Swap x and y: x = y − 7
  3. Solve for y: y = x + 7
11.Find the inverse function of f(x) = −5x − 5.

Answer: f−1(x) =

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

Answer: 4x − 17

  1. f(g(x)) = 4(x − 4) − 1
  2. = 4x − 17
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