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Year 11 Function Notation, Composites and Inverses Worksheet — Level 3 — Practice Set 3 — Answers

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

Answer: −8x + 21

  1. f(g(x)) = 4(−2x + 5) + 1
  2. = −8x + 21
2.Find the inverse function of f(x) = −4x − 8.

Answer: f−1(x) =

  1. y = −4x − 8
  2. Swap x and y: x = −4y − 8
  3. Solve for y: y =
3.Find the inverse function of f(x) = 4x.

Answer: f−1(x) =

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

Answer: 12x + 12

  1. g(f(x)) = −3(−4x − 6) − 6
  2. = 12x + 12
5.f(x) = 5x and g(x) = 5x + 1. Find g(f(x)) in simplest form.

Answer: 25x + 1

  1. g(f(x)) = 5(5x) + 1
  2. = 25x + 1
6.f(x) = 2x + 3 and g(x) = −4x + 1. Find f(g(x)) in simplest form.

Answer: −8x + 5

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

Answer: 20x − 5

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

Answer: f−1(x) =

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

Answer: −6x − 5

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

Answer: 6x − 1

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

Answer: −6x + 8

  1. g(f(x)) = −3(2x − 4) − 4
  2. = −6x + 8
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