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12th Grade Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 4 — Answers

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12th Grade Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 4 — 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 − 1 and g(x) = −x + 3. Find g(f(x)) in simplest form.

Answer: −5x + 4

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

Answer: 2x + 2

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

Answer: f−1(x) =

  1. y = −3x − 5
  2. Swap x and y: x = −3y − 5
  3. Solve for y: y =
5.Find the inverse function of f(x) = 7x + 8.

Answer: f−1(x) =

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

Answer: 3x − 7

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

Answer: −2x − 4

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

Answer: −9x + 21

  1. f(g(x)) = 3(−3x + 6) + 3
  2. = −9x + 21
9.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 =
10.f(x) = 3x + 3 and g(x) = x − 4. Find g(f(x)) in simplest form.

Answer: 3x − 1

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

Answer: −8x + 3

  1. f(g(x)) = −4(2x) + 3
  2. = −8x + 3
12.Find the inverse function of f(x) = 6x + 3.

Answer: f−1(x) =

  1. y = 6x + 3
  2. Swap x and y: x = 6y + 3
  3. Solve for y: y =
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