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10th Grade Function Notation, Composites and Inverses Worksheet — Level 3 — Answers

Answer sheet with worked solutions for the 10th Grade functions worksheet.

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10th 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) = x + 2 and g(x) = x − 6. Find f(g(x)) in simplest form.

Answer: x − 4

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

Answer: −6x + 7

  1. f(g(x)) = 3(−2x + 4) − 5
  2. = −6x + 7
3.Find the inverse function of f(x) = −x − 4.

Answer: f−1(x) = −x − 4

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

Answer: f−1(x) = −

  1. y = −2x
  2. Swap x and y: x = −2y
  3. Solve for y: y = −
5.Find the inverse function of f(x) = 4x + 9.

Answer: f−1(x) =

  1. y = 4x + 9
  2. Swap x and y: x = 4y + 9
  3. Solve for y: y =
6.Find the inverse function of f(x) = 3x + 3.

Answer: f−1(x) =

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

Answer: 6x − 1

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

Answer: 8x − 13

  1. g(f(x)) = −2(−4x + 4) − 5
  2. = 8x − 13
11.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 = −
12.f(x) = 5x − 4 and g(x) = −x + 3. Find g(f(x)) in simplest form.

Answer: −5x + 7

  1. g(f(x)) = −1(5x − 4) + 3
  2. = −5x + 7
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