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Grade 11 · Math

Compose two functions

Evaluate an inner function and use its result as the input of an outer function.

8 generated examples + worked example

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Worked example

Let f(x) = 3x − 4 and g(x) = x2. Find f(g(−2)).

Answer & why

Answer: 8

First g(−2) = 4, then f(4) = 3 × 4 − 4 = 8.

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Try these examples

8 reproducible examples from this math generator. Choose New examples for another set.

Question 1

Let f(x) = 3x + (2) and g(x) = x2. Find f(g(-2)).

  1. 13
  2. 14
  3. 16
  4. 18
A hint

Evaluate the inner function first; use its output as the input of the outer function.

Answer & why

Answer: 14

First g(-2) = (-2)2 = 4. Then f(4) = 3 × 4 + (2) = 14.

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Question 2

Let f(x) = 5x + (4) and g(x) = x2. Find f(g(-4)).

  1. 82
  2. 84
  3. 83
  4. 88
A hint

Evaluate the inner function first; use its output as the input of the outer function.

Answer & why

Answer: 84

First g(-4) = (-4)2 = 16. Then f(16) = 5 × 16 + (4) = 84.

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Question 3

Let f(x) = 2x + (-1) and g(x) = x2. Find f(g(-1)).

  1. 2
  2. 0
  3. 5
  4. 1
A hint

Evaluate the inner function first; use its output as the input of the outer function.

Answer & why

Answer: 1

First g(-1) = (-1)2 = 1. Then f(1) = 2 × 1 + (-1) = 1.

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Question 4

Let f(x) = 5x + (-5) and g(x) = x2. Find f(g(-1)).

  1. 2
  2. 3
  3. 1
  4. 0
A hint

Evaluate the inner function first; use its output as the input of the outer function.

Answer & why

Answer: 0

First g(-1) = (-1)2 = 1. Then f(1) = 5 × 1 + (-5) = 0.

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Question 5

Let f(x) = 3x + (4) and g(x) = x2. Find f(g(0)).

  1. 4
  2. 3
  3. 2
  4. 7
A hint

Evaluate the inner function first; use its output as the input of the outer function.

Answer & why

Answer: 4

First g(0) = (0)2 = 0. Then f(0) = 3 × 0 + (4) = 4.

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Question 6

Let f(x) = 2x + (4) and g(x) = x2. Find f(g(4)).

  1. 40
  2. 34
  3. 36
  4. 35
A hint

Evaluate the inner function first; use its output as the input of the outer function.

Answer & why

Answer: 36

First g(4) = (4)2 = 16. Then f(16) = 2 × 16 + (4) = 36.

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Question 7

Let f(x) = 4x + (-5) and g(x) = x2. Find f(g(0)).

  1. -2
  2. -4
  3. -5
  4. -3
A hint

Evaluate the inner function first; use its output as the input of the outer function.

Answer & why

Answer: -5

First g(0) = (0)2 = 0. Then f(0) = 4 × 0 + (-5) = -5.

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Question 8

Let f(x) = 6x + (-2) and g(x) = x2. Find f(g(-4)).

  1. 95
  2. 92
  3. 94
  4. 98
A hint

Evaluate the inner function first; use its output as the input of the outer function.

Answer & why

Answer: 94

First g(-4) = (-4)2 = 16. Then f(16) = 6 × 16 + (-2) = 94.

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