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11th Grade Function Notation, Composites and Inverses Worksheet — Level 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 — 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) = 5x − 4. Find f(g(x)) in simplest form.

Answer: 10x − 13

  1. f(g(x)) = 2(5x − 4) − 5
  2. = 10x − 13
2.f(x) = 4x − 3 and g(x) = 3x + 2. Find g(f(x)) in simplest form.

Answer: 12x − 7

  1. g(f(x)) = 3(4x − 3) + 2
  2. = 12x − 7
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.Find the inverse function of f(x) = 7x + 6.

Answer: f−1(x) =

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

Answer: −6x − 13

  1. f(g(x)) = −2(3x + 4) − 5
  2. = −6x − 13
6.f(x) = −x + 5 and g(x) = x − 6. Find g(f(x)) in simplest form.

Answer: −x − 1

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

Answer: 6x − 12

  1. f(g(x)) = −2(−3x + 3) − 6
  2. = 6x − 12
8.Find the inverse function of f(x) = −3x + 6.

Answer: f−1(x) =

  1. y = −3x + 6
  2. Swap x and y: x = −3y + 6
  3. Solve for y: y =
9.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 =
10.Find the inverse function of f(x) = x + 8.

Answer: f−1(x) = x − 8

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

Answer: 6x − 3

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

Answer: 6x − 5

  1. f(g(x)) = 2(3x − 2) − 1
  2. = 6x − 5
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